Right triangle trigonometry worksheet for Algebra 1

Right triangle trigonometry is mainly a Geometry topic, and some Algebra 1 courses preview it as three ratios of the sides of a right triangle, often remembered as SOH CAH TOA. Most questions give all three sides and ask for one ratio as a fraction in lowest terms; others use a special angle for an exact side, or a calculator for a trig value or an angle.

Also taught in Algebra 2, Precalculus and Geometry, 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.

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Sigma Prep · sigmaprep.io/worksheets Name Right Triangle Trigonometry Date Period Answer each question. Find the sine In right triangle $A B C$ , $∠ C = 90^{\circ}$ , $B C = 14$ , $A C = 48$ and $A B = 50$ . Find $\sin A$ . In right triangle $A B C$ , $∠ C = 90^{\circ}$ , $B C = 20$ , $A C = 48$ and $A B = 52$ . Find $\sin B$ . A right triangle has legs $12$ and $16$ and hypotenuse $20$ . Find $\sin A$ , where $A$ is opposite the side of length $16$ . A right triangle has legs $45$ and $24$ and hypotenuse $51$ . Find $\sin A$ , where $A$ is opposite the side of length $45$ . Find the cosine A right triangle has legs $8$ and $15$ and hypotenuse $17$ . Find $\cos A$ , where $A$ is opposite the side of length $15$ . In right triangle $A B C$ , $∠ C = 90^{\circ}$ , $B C = 15$ , $A C = 36$ and $A B = 39$ . Find $\cos B$ . In right triangle $A B C$ , $∠ C = 90^{\circ}$ , $B C = 126$ , $A C = 120$ and $A B = 174$ . Find $\cos A$ . A right triangle has legs $42$ and $40$ and hypotenuse $58$ . Find $\cos A$ , where $A$ is opposite the side of length $40$ . Find the tangent A right triangle has legs $21$ and $72$ and hypotenuse $75$ . Find $\tan A$ , where $A$ is opposite the side of length $21$ . A right triangle has legs $45$ and $24$ and hypotenuse $51$ . Find $\tan A$ , where $A$ is opposite the side of length $45$ . In right triangle $A B C$ , $∠ C = 90^{\circ}$ , $B C = 15$ , $A C = 8$ and $A B = 17$ . Find $\tan B$ . Find a side using a special angle A $38$ -ft ladder leans against a wall at $30^{\circ}$ to the ground. How far is its foot from the wall? Give an exact answer. A right triangle has hypotenuse $26$ and an angle of $45^{\circ}$ . Find the side $opposite$ it. Give an exact answer. In right triangle $A B C$ , $∠ C = 90^{\circ}$ , $∠ A = 60^{\circ}$ and $A B = 30$ . Find $B C$ . Give an exact answer. Find trig values and angles Find $\tan 20^{\circ}$ to four decimal places. Find $\sin 74^{\circ}$ to four decimal places. Find $\cos 73^{\circ}$ to four decimal places. Find the missing angle Find $m ∠ K$ 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
In right triangle $A B C$ , $∠ C = 90^{\circ}$ , $B C = 14$ , $A C = 48$ and $A B = 50$ . Find $\sin A$ .
In right triangle $A B C$ , $∠ C = 90^{\circ}$ , $B C = 20$ , $A C = 48$ and $A B = 52$ . Find $\sin B$ .
A right triangle has legs $12$ and $16$ and hypotenuse $20$ . Find $\sin A$ , where $A$ is opposite the side of length $16$ .
A right triangle has legs $45$ and $24$ and hypotenuse $51$ . Find $\sin A$ , where $A$ is opposite the side of length $45$ .

Find the cosine
A right triangle has legs $8$ and $15$ and hypotenuse $17$ . Find $\cos A$ , where $A$ is opposite the side of length $15$ .
In right triangle $A B C$ , $∠ C = 90^{\circ}$ , $B C = 15$ , $A C = 36$ and $A B = 39$ . Find $\cos B$ .
In right triangle $A B C$ , $∠ C = 90^{\circ}$ , $B C = 126$ , $A C = 120$ and $A B = 174$ . Find $\cos A$ .
A right triangle has legs $42$ and $40$ and hypotenuse $58$ . Find $\cos A$ , where $A$ is opposite the side of length $40$ .

Find the tangent
A right triangle has legs $21$ and $72$ and hypotenuse $75$ . Find $\tan A$ , where $A$ is opposite the side of length $21$ .
A right triangle has legs $45$ and $24$ and hypotenuse $51$ . Find $\tan A$ , where $A$ is opposite the side of length $45$ .
In right triangle $A B C$ , $∠ C = 90^{\circ}$ , $B C = 15$ , $A C = 8$ and $A B = 17$ . Find $\tan B$ .

Find a side using a special angle
A $38$ -ft ladder leans against a wall at $30^{\circ}$ to the ground. How far is its foot from the wall? Give an exact answer.
A right triangle has hypotenuse $26$ and an angle of $45^{\circ}$ . Find the side $opposite$ it. Give an exact answer.
In right triangle $A B C$ , $∠ C = 90^{\circ}$ , $∠ A = 60^{\circ}$ and $A B = 30$ . Find $B C$ . Give an exact answer.

Find trig values and angles
Find $\tan 20^{\circ}$ to four decimal places.
Find $\sin 74^{\circ}$ to four decimal places.
Find $\cos 73^{\circ}$ to four decimal places.

Find the missing angle
Find $m ∠ K$ 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 4 Date Period Answer each question. Find the sine In right triangle $A B C$ , $∠ C = 90^{\circ}$ , $B C = 14$ , $A C = 48$ and $A B = 50$ . Find $\sin A$ . $\frac{7}{25}$ In right triangle $A B C$ , $∠ C = 90^{\circ}$ , $B C = 20$ , $A C = 48$ and $A B = 52$ . Find $\sin B$ . $\frac{12}{13}$ A right triangle has legs $12$ and $16$ and hypotenuse $20$ . Find $\sin A$ , where $A$ is opposite the side of length $16$ . $\frac{4}{5}$ A right triangle has legs $45$ and $24$ and hypotenuse $51$ . Find $\sin A$ , where $A$ is opposite the side of length $45$ . $\frac{15}{17}$ Find the cosine A right triangle has legs $8$ and $15$ and hypotenuse $17$ . Find $\cos A$ , where $A$ is opposite the side of length $15$ . $\frac{8}{17}$ In right triangle $A B C$ , $∠ C = 90^{\circ}$ , $B C = 15$ , $A C = 36$ and $A B = 39$ . Find $\cos B$ . $\frac{5}{13}$ In right triangle $A B C$ , $∠ C = 90^{\circ}$ , $B C = 126$ , $A C = 120$ and $A B = 174$ . Find $\cos A$ . $\frac{20}{29}$ A right triangle has legs $42$ and $40$ and hypotenuse $58$ . Find $\cos A$ , where $A$ is opposite the side of length $40$ . $\frac{21}{29}$ Find the tangent A right triangle has legs $21$ and $72$ and hypotenuse $75$ . Find $\tan A$ , where $A$ is opposite the side of length $21$ . $\frac{7}{24}$ A right triangle has legs $45$ and $24$ and hypotenuse $51$ . Find $\tan A$ , where $A$ is opposite the side of length $45$ . $\frac{15}{8}$ In right triangle $A B C$ , $∠ C = 90^{\circ}$ , $B C = 15$ , $A C = 8$ and $A B = 17$ . Find $\tan B$ . $\frac{8}{15}$ Find a side using a special angle A $38$ -ft ladder leans against a wall at $30^{\circ}$ to the ground. How far is its foot from the wall? Give an exact answer. $19 \sqrt{3}$ A right triangle has hypotenuse $26$ and an angle of $45^{\circ}$ . Find the side $opposite$ it. Give an exact answer. $13 \sqrt{2}$ In right triangle $A B C$ , $∠ C = 90^{\circ}$ , $∠ A = 60^{\circ}$ and $A B = 30$ . Find $B C$ . Give an exact answer. $15 \sqrt{3}$ Find trig values and angles Find $\tan 20^{\circ}$ to four decimal places. $0.3640$ Find $\sin 74^{\circ}$ to four decimal places. $0.9613$ Find $\cos 73^{\circ}$ to four decimal places. $0.2924$ Find the missing angle Find $m ∠ K$ to the nearest tenth of a degree. ${43.6}^{\circ}$ Find $θ$ to the nearest tenth of a degree. ${73.7}^{\circ}$ Use the three sides to find $θ$ , to the nearest tenth of a degree. ${61.9}^{\circ}$ Free math worksheets at sigmaprep.io/worksheets© 2026 Sigma Prep

Sigma Prep · sigmaprep.io/worksheets

Name

Right Triangle TrigonometryAnswer keyVersion 4

Date Period

Answer each question.

Find the sine
In right triangle $A B C$ , $∠ C = 90^{\circ}$ , $B C = 14$ , $A C = 48$ and $A B = 50$ . Find $\sin A$ . $\frac{7}{25}$
In right triangle $A B C$ , $∠ C = 90^{\circ}$ , $B C = 20$ , $A C = 48$ and $A B = 52$ . Find $\sin B$ . $\frac{12}{13}$
A right triangle has legs $12$ and $16$ and hypotenuse $20$ . Find $\sin A$ , where $A$ is opposite the side of length $16$ . $\frac{4}{5}$
A right triangle has legs $45$ and $24$ and hypotenuse $51$ . Find $\sin A$ , where $A$ is opposite the side of length $45$ . $\frac{15}{17}$

Find the cosine
A right triangle has legs $8$ and $15$ and hypotenuse $17$ . Find $\cos A$ , where $A$ is opposite the side of length $15$ . $\frac{8}{17}$
In right triangle $A B C$ , $∠ C = 90^{\circ}$ , $B C = 15$ , $A C = 36$ and $A B = 39$ . Find $\cos B$ . $\frac{5}{13}$
In right triangle $A B C$ , $∠ C = 90^{\circ}$ , $B C = 126$ , $A C = 120$ and $A B = 174$ . Find $\cos A$ . $\frac{20}{29}$
A right triangle has legs $42$ and $40$ and hypotenuse $58$ . Find $\cos A$ , where $A$ is opposite the side of length $40$ . $\frac{21}{29}$

Find the tangent
A right triangle has legs $21$ and $72$ and hypotenuse $75$ . Find $\tan A$ , where $A$ is opposite the side of length $21$ . $\frac{7}{24}$
A right triangle has legs $45$ and $24$ and hypotenuse $51$ . Find $\tan A$ , where $A$ is opposite the side of length $45$ . $\frac{15}{8}$
In right triangle $A B C$ , $∠ C = 90^{\circ}$ , $B C = 15$ , $A C = 8$ and $A B = 17$ . Find $\tan B$ . $\frac{8}{15}$

Find a side using a special angle
A $38$ -ft ladder leans against a wall at $30^{\circ}$ to the ground. How far is its foot from the wall? Give an exact answer. $19 \sqrt{3}$
A right triangle has hypotenuse $26$ and an angle of $45^{\circ}$ . Find the side $opposite$ it. Give an exact answer. $13 \sqrt{2}$
In right triangle $A B C$ , $∠ C = 90^{\circ}$ , $∠ A = 60^{\circ}$ and $A B = 30$ . Find $B C$ . Give an exact answer. $15 \sqrt{3}$

Find trig values and angles
Find $\tan 20^{\circ}$ to four decimal places. $0.3640$
Find $\sin 74^{\circ}$ to four decimal places. $0.9613$
Find $\cos 73^{\circ}$ to four decimal places. $0.2924$

Find the missing angle
Find $m ∠ K$ to the nearest tenth of a degree. ${43.6}^{\circ}$
Find $θ$ to the nearest tenth of a degree. ${73.7}^{\circ}$
Use the three sides to find $θ$ , to the nearest tenth of a degree. ${61.9}^{\circ}$

How to do these

A right triangle has hypotenuse $20$ and an angle of $30^{\circ}$ . Find the side opposite it

Opposite and hypotenuse means sine: sin 30° = x/20.
sin 30° = 1/2, so x = 20 × 1/2.

The answer is $10$ .

Where students go wrong

Leaving the calculator in radian mode. sin 35 in radians is about -0.43, which gives a negative side length; switch to degrees first.

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.

Algebra 1 is usually taken around 8th or 9th 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 Algebra 1

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

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

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