Right triangle trigonometry worksheet for Precalculus

In Precalculus right triangle ratios are the starting point for the unit circle: sine, cosine and tangent from the three sides, exact sides from special angles, and angles found with an inverse function and rounded to the tenth of a degree.

Also taught in Algebra 2, Geometry and Algebra 1, each at its own level and with its own examples.

Not quite the one you need? Same words, different skill:

Special Right Triangles (Geometry). 45-45-90 and 30-60-90.

Select your difficulty

Pick more than one for a sheet that mixes them.

Question order

Difficulty

Printing options

Working space

Answer key

Print an answer key on a second page

Version

On the answer key. Type it in to get that sheet back.

Download PDF Print instead

Free, no account. Make as many different versions as you need.

The preview can look cramped on a phone. The PDF and printed sheet come out normal.



Sigma Prep · sigmaprep.io/worksheets Name Right Triangle Trigonometry Date Period Answer each question. Find the sine A right triangle has legs $180$ and $33$ and hypotenuse $183$ . Find $\sin A$ , where $A$ is opposite the side of length $33$ . In right triangle $A B C$ , $∠ C = 90^{\circ}$ , $B C = 30$ , $A C = 16$ and $A B = 34$ . Find $\sin B$ . In right triangle $A B C$ , $∠ C = 90^{\circ}$ , $B C = 360$ , $A C = 66$ and $A B = 366$ . Find $\sin A$ . A right triangle has legs $60$ and $63$ and hypotenuse $87$ . Find $\sin A$ , where $A$ is opposite the side of length $60$ . Find the cosine In right triangle $A B C$ , $∠ C = 90^{\circ}$ , $B C = 33$ , $A C = 56$ and $A B = 65$ . Find $\cos A$ . A right triangle has legs $385$ and $336$ and hypotenuse $511$ . Find $\cos A$ , where $A$ is opposite the side of length $336$ . A right triangle has legs $105$ and $36$ and hypotenuse $111$ . Find $\cos A$ , where $A$ is opposite the side of length $105$ . In right triangle $A B C$ , $∠ C = 90^{\circ}$ , $B C = 140$ , $A C = 48$ and $A B = 148$ . Find $\cos B$ . Find the tangent A right triangle has legs $220$ and $192$ and hypotenuse $292$ . Find $\tan A$ , where $A$ is opposite the side of length $220$ . In right triangle $A B C$ , $∠ C = 90^{\circ}$ , $B C = 300$ , $A C = 55$ and $A B = 305$ . Find $\tan B$ . In right triangle $A B C$ , $∠ C = 90^{\circ}$ , $B C = 168$ , $A C = 160$ and $A B = 232$ . Find $\tan A$ . Find a side using a special angle In right triangle $P Q R$ , the right angle is at $R$ , $∠ P = 30^{\circ}$ and $P R = 36$ . Find $P Q$ . Give an exact answer. A right triangle has a $60^{\circ}$ angle, and the leg $adjacent to$ it is $6$ . Find the other leg. Give an exact answer. A guy wire from the top of a pole meets the ground at $45^{\circ}$ . The pole is $12$ ft tall. Find the length of the wire, exactly. Find trig values and angles $\cos θ = 0.1$ . Find $θ$ to the nearest tenth of a degree. Find $\cos 20^{\circ}$ to four decimal places. $\sin θ = 0.421$ . Find $θ$ to the nearest tenth of a degree. Find the missing angle Find $m ∠ E$ to the nearest tenth of a degree. Find $θ$ to the nearest tenth of a degree. Use the three sides to find $θ$ , to the nearest tenth of a degree. Free math worksheets at sigmaprep.io/worksheets© 2026 Sigma Prep

Sigma Prep · sigmaprep.io/worksheets

Name

Right Triangle Trigonometry

Date Period

Answer each question.

Find the sine
A right triangle has legs $180$ and $33$ and hypotenuse $183$ . Find $\sin A$ , where $A$ is opposite the side of length $33$ .
In right triangle $A B C$ , $∠ C = 90^{\circ}$ , $B C = 30$ , $A C = 16$ and $A B = 34$ . Find $\sin B$ .
In right triangle $A B C$ , $∠ C = 90^{\circ}$ , $B C = 360$ , $A C = 66$ and $A B = 366$ . Find $\sin A$ .
A right triangle has legs $60$ and $63$ and hypotenuse $87$ . Find $\sin A$ , where $A$ is opposite the side of length $60$ .

Find the cosine
In right triangle $A B C$ , $∠ C = 90^{\circ}$ , $B C = 33$ , $A C = 56$ and $A B = 65$ . Find $\cos A$ .
A right triangle has legs $385$ and $336$ and hypotenuse $511$ . Find $\cos A$ , where $A$ is opposite the side of length $336$ .
A right triangle has legs $105$ and $36$ and hypotenuse $111$ . Find $\cos A$ , where $A$ is opposite the side of length $105$ .
In right triangle $A B C$ , $∠ C = 90^{\circ}$ , $B C = 140$ , $A C = 48$ and $A B = 148$ . Find $\cos B$ .

Find the tangent
A right triangle has legs $220$ and $192$ and hypotenuse $292$ . Find $\tan A$ , where $A$ is opposite the side of length $220$ .
In right triangle $A B C$ , $∠ C = 90^{\circ}$ , $B C = 300$ , $A C = 55$ and $A B = 305$ . Find $\tan B$ .
In right triangle $A B C$ , $∠ C = 90^{\circ}$ , $B C = 168$ , $A C = 160$ and $A B = 232$ . Find $\tan A$ .

Find a side using a special angle
In right triangle $P Q R$ , the right angle is at $R$ , $∠ P = 30^{\circ}$ and $P R = 36$ . Find $P Q$ . Give an exact answer.
A right triangle has a $60^{\circ}$ angle, and the leg $adjacent to$ it is $6$ . Find the other leg. Give an exact answer.
A guy wire from the top of a pole meets the ground at $45^{\circ}$ . The pole is $12$ ft tall. Find the length of the wire, exactly.

Find trig values and angles
$\cos θ = 0.1$ . Find $θ$ to the nearest tenth of a degree.
Find $\cos 20^{\circ}$ to four decimal places.
$\sin θ = 0.421$ . Find $θ$ to the nearest tenth of a degree.

Find the missing angle
Find $m ∠ E$ to the nearest tenth of a degree.
Find $θ$ to the nearest tenth of a degree.
Use the three sides to find $θ$ , to the nearest tenth of a degree.



Sigma Prep · sigmaprep.io/worksheets Name Right Triangle TrigonometryAnswer keyVersion 2 Date Period Answer each question. Find the sine A right triangle has legs $180$ and $33$ and hypotenuse $183$ . Find $\sin A$ , where $A$ is opposite the side of length $33$ . $\frac{11}{61}$ In right triangle $A B C$ , $∠ C = 90^{\circ}$ , $B C = 30$ , $A C = 16$ and $A B = 34$ . Find $\sin B$ . $\frac{8}{17}$ In right triangle $A B C$ , $∠ C = 90^{\circ}$ , $B C = 360$ , $A C = 66$ and $A B = 366$ . Find $\sin A$ . $\frac{60}{61}$ A right triangle has legs $60$ and $63$ and hypotenuse $87$ . Find $\sin A$ , where $A$ is opposite the side of length $60$ . $\frac{20}{29}$ Find the cosine In right triangle $A B C$ , $∠ C = 90^{\circ}$ , $B C = 33$ , $A C = 56$ and $A B = 65$ . Find $\cos A$ . $\frac{56}{65}$ A right triangle has legs $385$ and $336$ and hypotenuse $511$ . Find $\cos A$ , where $A$ is opposite the side of length $336$ . $\frac{55}{73}$ A right triangle has legs $105$ and $36$ and hypotenuse $111$ . Find $\cos A$ , where $A$ is opposite the side of length $105$ . $\frac{12}{37}$ In right triangle $A B C$ , $∠ C = 90^{\circ}$ , $B C = 140$ , $A C = 48$ and $A B = 148$ . Find $\cos B$ . $\frac{35}{37}$ Find the tangent A right triangle has legs $220$ and $192$ and hypotenuse $292$ . Find $\tan A$ , where $A$ is opposite the side of length $220$ . $\frac{55}{48}$ In right triangle $A B C$ , $∠ C = 90^{\circ}$ , $B C = 300$ , $A C = 55$ and $A B = 305$ . Find $\tan B$ . $\frac{11}{60}$ In right triangle $A B C$ , $∠ C = 90^{\circ}$ , $B C = 168$ , $A C = 160$ and $A B = 232$ . Find $\tan A$ . $\frac{21}{20}$ Find a side using a special angle In right triangle $P Q R$ , the right angle is at $R$ , $∠ P = 30^{\circ}$ and $P R = 36$ . Find $P Q$ . Give an exact answer. $24 \sqrt{3}$ A right triangle has a $60^{\circ}$ angle, and the leg $adjacent to$ it is $6$ . Find the other leg. Give an exact answer. $6 \sqrt{3}$ A guy wire from the top of a pole meets the ground at $45^{\circ}$ . The pole is $12$ ft tall. Find the length of the wire, exactly. $12 \sqrt{2}$ Find trig values and angles $\cos θ = 0.1$ . Find $θ$ to the nearest tenth of a degree. ${84.3}^{\circ}$ Find $\cos 20^{\circ}$ to four decimal places. $0.9397$ $\sin θ = 0.421$ . Find $θ$ to the nearest tenth of a degree. ${24.9}^{\circ}$ Find the missing angle Find $m ∠ E$ to the nearest tenth of a degree. ${34.2}^{\circ}$ Find $θ$ to the nearest tenth of a degree. ${48.9}^{\circ}$ Use the three sides to find $θ$ , to the nearest tenth of a degree. ${69.4}^{\circ}$ Free math worksheets at sigmaprep.io/worksheets© 2026 Sigma Prep

Sigma Prep · sigmaprep.io/worksheets

Name

Right Triangle TrigonometryAnswer keyVersion 2

Date Period

Answer each question.

Find the sine
A right triangle has legs $180$ and $33$ and hypotenuse $183$ . Find $\sin A$ , where $A$ is opposite the side of length $33$ . $\frac{11}{61}$
In right triangle $A B C$ , $∠ C = 90^{\circ}$ , $B C = 30$ , $A C = 16$ and $A B = 34$ . Find $\sin B$ . $\frac{8}{17}$
In right triangle $A B C$ , $∠ C = 90^{\circ}$ , $B C = 360$ , $A C = 66$ and $A B = 366$ . Find $\sin A$ . $\frac{60}{61}$
A right triangle has legs $60$ and $63$ and hypotenuse $87$ . Find $\sin A$ , where $A$ is opposite the side of length $60$ . $\frac{20}{29}$

Find the cosine
In right triangle $A B C$ , $∠ C = 90^{\circ}$ , $B C = 33$ , $A C = 56$ and $A B = 65$ . Find $\cos A$ . $\frac{56}{65}$
A right triangle has legs $385$ and $336$ and hypotenuse $511$ . Find $\cos A$ , where $A$ is opposite the side of length $336$ . $\frac{55}{73}$
A right triangle has legs $105$ and $36$ and hypotenuse $111$ . Find $\cos A$ , where $A$ is opposite the side of length $105$ . $\frac{12}{37}$
In right triangle $A B C$ , $∠ C = 90^{\circ}$ , $B C = 140$ , $A C = 48$ and $A B = 148$ . Find $\cos B$ . $\frac{35}{37}$

Find the tangent
A right triangle has legs $220$ and $192$ and hypotenuse $292$ . Find $\tan A$ , where $A$ is opposite the side of length $220$ . $\frac{55}{48}$
In right triangle $A B C$ , $∠ C = 90^{\circ}$ , $B C = 300$ , $A C = 55$ and $A B = 305$ . Find $\tan B$ . $\frac{11}{60}$
In right triangle $A B C$ , $∠ C = 90^{\circ}$ , $B C = 168$ , $A C = 160$ and $A B = 232$ . Find $\tan A$ . $\frac{21}{20}$

Find a side using a special angle
In right triangle $P Q R$ , the right angle is at $R$ , $∠ P = 30^{\circ}$ and $P R = 36$ . Find $P Q$ . Give an exact answer. $24 \sqrt{3}$
A right triangle has a $60^{\circ}$ angle, and the leg $adjacent to$ it is $6$ . Find the other leg. Give an exact answer. $6 \sqrt{3}$
A guy wire from the top of a pole meets the ground at $45^{\circ}$ . The pole is $12$ ft tall. Find the length of the wire, exactly. $12 \sqrt{2}$

Find trig values and angles
$\cos θ = 0.1$ . Find $θ$ to the nearest tenth of a degree. ${84.3}^{\circ}$
Find $\cos 20^{\circ}$ to four decimal places. $0.9397$
$\sin θ = 0.421$ . Find $θ$ to the nearest tenth of a degree. ${24.9}^{\circ}$

Find the missing angle
Find $m ∠ E$ to the nearest tenth of a degree. ${34.2}^{\circ}$
Find $θ$ to the nearest tenth of a degree. ${48.9}^{\circ}$
Use the three sides to find $θ$ , to the nearest tenth of a degree. ${69.4}^{\circ}$

How to do these

A right triangle has legs $20$ and $21$ and hypotenuse $29$ . Find $\tan A$ , where $A$ is opposite the side of length $20$

Tangent is opposite over adjacent.
The side opposite A is 20 and the leg next to it is 21.

The answer is $\frac{20}{21}$ .

Where students go wrong

Using the hypotenuse in tangent. Tangent is opposite over adjacent, the two legs; only sine and cosine have the hypotenuse on the bottom.

Also called SOHCAHTOA, trig ratios or finding missing sides.

What you can put on this worksheet

Sine from the three sides: In right triangle $A B C$ , $∠ C = 90^{\circ}$ , $B C = 45$ , $A C = 24$ and $A B = 51$ . Find $\sin A$ . → $\frac{15}{17}$
Cosine from the three sides: In right triangle $A B C$ , $∠ C = 90^{\circ}$ , $B C = 45$ , $A C = 24$ and $A B = 51$ . Find $\cos A$ . → $\frac{8}{17}$
Tangent from the three sides: In right triangle $A B C$ , $∠ C = 90^{\circ}$ , $B C = 45$ , $A C = 24$ and $A B = 51$ . Find $\tan A$ . → $\frac{15}{8}$
A missing side from a special angle: A right triangle has hypotenuse $12$ and an angle of $45^{\circ}$ . Find the side $adjacent to$ it. Give an exact answer. → $6 \sqrt{2}$
Cosecant, secant and cotangent from the sides: A right triangle has legs $45$ and $24$ and hypotenuse $51$ . Find $\csc A$ , where $A$ is opposite the side of length $45$ → $\frac{17}{15}$
A missing side, any angle, rounded: Find the length $x$ to the nearest tenth. — a right triangle with a 47° angle, legs 13 and x, hypotenuse unknown → $13.9$
An angle from two sides, with inverse trig: Find $θ$ . Round to the nearest degree. — a right triangle with a θ angle, legs 20 and 13, hypotenuse unknown → $33^{\circ}$
Ratios and angles on a calculator: Find $\cos 50^{\circ}$ to four decimal places. → $0.6428$
All three sides given: find the angle: Use the three sides to find $θ$ , to the nearest tenth of a degree. — a right triangle, labeled 34, 30, 16, θ → ${28.1}^{\circ}$
A ratio read off a drawing, as a fraction: Find $\cos A$ . — a right triangle, labeled 34, 30, 16, A, B, C → $\frac{8}{17}$
A ratio read off a drawing, to four decimal places: Find $\cos S$ to four decimal places. — a right triangle, labeled 17, 15, 8, S, T, U → $0.4706$
One ratio given, find another: Angle $A$ is acute and $\tan A = \frac{40}{9}$ . Find $\sin A$ → $\frac{40}{41}$
Sides with roots, csc sec cot values, from one ratio to another: Find the value to four decimal places: $\cot ⁣ (11^{\circ})$ → $5.1446$
Calculator values in radians: In radian mode, find $\cos (3 π / 10)$ , to four decimal places. → $0.5878$

Questions about these worksheets

Yes. Every right triangle trigonometry sheet is free to print and free to download as a PDF. There is no account to make, no email to hand over and no limit on how many you take.

Yes. The answer key prints on a second page, and you can choose whether it shows each question beside its answer or just the answers in a list.

Yes. Print straight from the page, or download the PDF and print that. The sheet is laid out for paper rather than squeezed off a screen, so there is room to work under each question, and the answer key comes out on its own page.

Precalculus is usually taken around 11th or 12th grade, though schools vary and plenty of students meet it earlier or later. Pick the difficulty rather than the grade: the easy level suits a first lesson on it, the hard level suits review before a test.

Yes, as many as you like. The questions are built fresh each time rather than picked from a fixed set of files, so pressing Generate gives a new sheet. That is what you want for a second class, a retake, or two students sitting next to each other.

That is the closest comparison, and Kuta Software is good software. It is also paid software you install on a computer. These worksheets run in a browser tab for free, with no account and nothing to install. Like Kuta, the right triangle trigonometry questions are generated when you ask for them rather than pulled from a fixed set of files, so two classes never get the same sheet, and the answer key comes with it.

Yes. There are two levels, and you can tick more than one for a sheet that mixes them, in which case the questions come out easiest first. The harder levels are not just larger numbers: they ask for something the easy ones do not.

You pick from 14: sine from the three sides, cosine from the three sides, tangent from the three sides, a missing side from a special angle, cosecant, secant and cotangent from the sides, a missing side, any angle, rounded, an angle from two sides, with inverse trig, ratios and angles on a calculator, all three sides given: find the angle, a ratio read off a drawing, as a fraction, a ratio read off a drawing, to four decimal places, one ratio given, find another, sides with roots, csc sec cot values, from one ratio to another and calculator values in radians. Tick as many as you want and set how many of each, or let it spread them evenly.

Using the hypotenuse as the adjacent side. The hypotenuse is never the adjacent one: adjacent means the leg next to the angle, and the hypotenuse has its own name for a reason.

Right triangle trigonometry worksheet for Precalculus

Select your difficulty

Find the sine

Find the cosine

Find the tangent

Find a side using a special angle

Find trig values and angles

Find the missing angle

Find the sine

Find the cosine

Find the tangent

Find a side using a special angle

Find trig values and angles

Find the missing angle

How to do these

Where students go wrong

What you can put on this worksheet

Questions about these worksheets

Are these right triangle trigonometry worksheets free?+

Do the right triangle trigonometry worksheets come with an answer key?+

Are these right triangle trigonometry worksheets printable?+

What grade are these right triangle trigonometry worksheets for?+

Can I get a different version of the same right triangle trigonometry worksheet?+

Is this a free alternative to Kuta Software for right triangle trigonometry?+

Can I choose how hard the right triangle trigonometry questions are?+

What kinds of question are on a right triangle trigonometry worksheet?+

What do students get wrong with right triangle trigonometry?+