Solve right triangle ABC with C = 90°, A = 50°, a = 14. Round sides to the nearest tenth.

B = 40°, b is about 11.7, c is about 18.3

In right triangle ABC, C = 90°, B = 36° and c = 21. Find A, a and b. Round the sides to the nearest tenth.

A = 54°, a is about 17.0, b is about 12.3

In right triangle ABC, C = 90°, A = 56° and a = 13. Find B, b and c. Round the sides to the nearest tenth.

B = 34°, b is about 8.8, c is about 15.7

Solve right triangle ABC with C = 90°, B = 37°, c = 24. Round sides to the nearest tenth.

A = 53°, a is about 19.2, b is about 14.4

Solve right triangle ABC with C = 90°, B = 47°, b = 24. Round sides to the nearest tenth.

A = 43°, a is about 22.4, c is about 32.8

Worksheets · Geometry

Solving right triangles worksheet for Geometry

Pick the ratio that joins the side you have to the side you want, then use a calculator. To find an angle, set up the ratio from two sides and use the inverse: sin⁻¹, cos⁻¹ or tan⁻¹. The special triangles, where the angles come out exact, are here too.

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

Select your difficulty

Pick more than one for a sheet that mixes them.

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



Sigma Prep · sigmaprep.io/worksheets Name Solving Right Triangles Date Period Find each measure. Find the missing side Find $x$ . Round to the nearest tenth. Solve for $x$ . Round your answer to the nearest tenth. Find the length $x$ to the nearest tenth. Find $x$ . Round to the nearest tenth. Find the missing angle Find $θ$ . Round to the nearest degree. Find $m ∠ M$ to the nearest tenth of a degree. Find $θ$ . Round to the nearest degree. Use the three sides to find $θ$ , to the nearest tenth of a degree. Find $θ$ . Round to the nearest degree. Find $θ$ to the nearest tenth of a degree. Find $θ$ . Round to the nearest degree. Find $θ$ to the nearest tenth of a degree. Find an acute angle exactly A right triangle has legs $9$ and $9$ . Find the acute angles. A right triangle has legs $7$ and $7 \sqrt{3}$ . Find the larger acute angle. A right triangle has legs $9$ and $9 \sqrt{3}$ . Find the smaller acute angle. A right triangle has legs $6$ and $6 \sqrt{3}$ . Find the larger acute angle. Solve the right triangle Solve right triangle $A B C$ with $C = 90^{\circ}$ , $A = 50^{\circ}$ , $a = 14$ . Round sides to the nearest tenth. In right triangle $A B C$ , $C = 90^{\circ}$ , $B = 36^{\circ}$ and $c = 21$ . Find $A$ , $a$ and $b$ . Round the sides to the nearest tenth. In right triangle $A B C$ , $C = 90^{\circ}$ , $A = 56^{\circ}$ and $a = 13$ . Find $B$ , $b$ and $c$ . Round the sides to the nearest tenth. Solve right triangle $A B C$ with $C = 90^{\circ}$ , $B = 37^{\circ}$ , $c = 24$ . Round sides to the nearest tenth. Free math worksheets at sigmaprep.io/worksheets© 2026 Sigma Prep

Sigma Prep · sigmaprep.io/worksheets

Name

Solving Right Triangles

Date Period

Find each measure.

Find the missing side
Find $x$ . Round to the nearest tenth.
Solve for $x$ . Round your answer to the nearest tenth.
Find the length $x$ to the nearest tenth.
Find $x$ . Round to the nearest tenth.

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

Find an acute angle exactly
A right triangle has legs $9$ and $9$ . Find the acute angles.
A right triangle has legs $7$ and $7 \sqrt{3}$ . Find the larger acute angle.
A right triangle has legs $9$ and $9 \sqrt{3}$ . Find the smaller acute angle.
A right triangle has legs $6$ and $6 \sqrt{3}$ . Find the larger acute angle.

Solve the right triangle
Solve right triangle $A B C$ with $C = 90^{\circ}$ , $A = 50^{\circ}$ , $a = 14$ . Round sides to the nearest tenth.
In right triangle $A B C$ , $C = 90^{\circ}$ , $B = 36^{\circ}$ and $c = 21$ . Find $A$ , $a$ and $b$ . Round the sides to the nearest tenth.
In right triangle $A B C$ , $C = 90^{\circ}$ , $A = 56^{\circ}$ and $a = 13$ . Find $B$ , $b$ and $c$ . Round the sides to the nearest tenth.
Solve right triangle $A B C$ with $C = 90^{\circ}$ , $B = 37^{\circ}$ , $c = 24$ . Round sides to the nearest tenth.



Sigma Prep · sigmaprep.io/worksheets Name Solving Right TrianglesAnswer keyVersion 1 Date Period Find each measure. Find the missing side Find $x$ . Round to the nearest tenth. $12.5$ Solve for $x$ . Round your answer to the nearest tenth. $4.8$ Find the length $x$ to the nearest tenth. $7.4$ Find $x$ . Round to the nearest tenth. $11.3$ Find the missing angle Find $θ$ . Round to the nearest degree. $53^{\circ}$ Find $m ∠ M$ to the nearest tenth of a degree. ${22.6}^{\circ}$ Find $θ$ . Round to the nearest degree. $48^{\circ}$ Use the three sides to find $θ$ , to the nearest tenth of a degree. ${73.7}^{\circ}$ Find $θ$ . Round to the nearest degree. $29^{\circ}$ Find $θ$ to the nearest tenth of a degree. ${53.1}^{\circ}$ Find $θ$ . Round to the nearest degree. $58^{\circ}$ Find $θ$ to the nearest tenth of a degree. ${61.9}^{\circ}$ Find an acute angle exactly A right triangle has legs $9$ and $9$ . Find the acute angles. $45^{\circ}$ and $45^{\circ}$ A right triangle has legs $7$ and $7 \sqrt{3}$ . Find the larger acute angle. $60^{\circ}$ A right triangle has legs $9$ and $9 \sqrt{3}$ . Find the smaller acute angle. $30^{\circ}$ A right triangle has legs $6$ and $6 \sqrt{3}$ . Find the larger acute angle. $60^{\circ}$ Solve the right triangle Solve right triangle $A B C$ with $C = 90^{\circ}$ , $A = 50^{\circ}$ , $a = 14$ . Round sides to the nearest tenth. $B = 40^{\circ}$ , $b \approx 11.7$ , $c \approx 18.3$ In right triangle $A B C$ , $C = 90^{\circ}$ , $B = 36^{\circ}$ and $c = 21$ . Find $A$ , $a$ and $b$ . Round the sides to the nearest tenth. $A = 54^{\circ}$ , $a \approx 17.0$ , $b \approx 12.3$ In right triangle $A B C$ , $C = 90^{\circ}$ , $A = 56^{\circ}$ and $a = 13$ . Find $B$ , $b$ and $c$ . Round the sides to the nearest tenth. $B = 34^{\circ}$ , $b \approx 8.8$ , $c \approx 15.7$ Solve right triangle $A B C$ with $C = 90^{\circ}$ , $B = 37^{\circ}$ , $c = 24$ . Round sides to the nearest tenth. $A = 53^{\circ}$ , $a \approx 19.2$ , $b \approx 14.4$ Free math worksheets at sigmaprep.io/worksheets© 2026 Sigma Prep

Sigma Prep · sigmaprep.io/worksheets

Name

Solving Right TrianglesAnswer keyVersion 1

Date Period

Find each measure.

Find the missing side
Find $x$ . Round to the nearest tenth. $12.5$
Solve for $x$ . Round your answer to the nearest tenth. $4.8$
Find the length $x$ to the nearest tenth. $7.4$
Find $x$ . Round to the nearest tenth. $11.3$

Find the missing angle
Find $θ$ . Round to the nearest degree. $53^{\circ}$
Find $m ∠ M$ to the nearest tenth of a degree. ${22.6}^{\circ}$
Find $θ$ . Round to the nearest degree. $48^{\circ}$
Use the three sides to find $θ$ , to the nearest tenth of a degree. ${73.7}^{\circ}$
Find $θ$ . Round to the nearest degree. $29^{\circ}$
Find $θ$ to the nearest tenth of a degree. ${53.1}^{\circ}$
Find $θ$ . Round to the nearest degree. $58^{\circ}$
Find $θ$ to the nearest tenth of a degree. ${61.9}^{\circ}$

Find an acute angle exactly
A right triangle has legs $9$ and $9$ . Find the acute angles. $45^{\circ}$ and $45^{\circ}$
A right triangle has legs $7$ and $7 \sqrt{3}$ . Find the larger acute angle. $60^{\circ}$
A right triangle has legs $9$ and $9 \sqrt{3}$ . Find the smaller acute angle. $30^{\circ}$
A right triangle has legs $6$ and $6 \sqrt{3}$ . Find the larger acute angle. $60^{\circ}$

Solve the right triangle
Solve right triangle $A B C$ with $C = 90^{\circ}$ , $A = 50^{\circ}$ , $a = 14$ . Round sides to the nearest tenth. $B = 40^{\circ}$ , $b \approx 11.7$ , $c \approx 18.3$
In right triangle $A B C$ , $C = 90^{\circ}$ , $B = 36^{\circ}$ and $c = 21$ . Find $A$ , $a$ and $b$ . Round the sides to the nearest tenth. $A = 54^{\circ}$ , $a \approx 17.0$ , $b \approx 12.3$
In right triangle $A B C$ , $C = 90^{\circ}$ , $A = 56^{\circ}$ and $a = 13$ . Find $B$ , $b$ and $c$ . Round the sides to the nearest tenth. $B = 34^{\circ}$ , $b \approx 8.8$ , $c \approx 15.7$
Solve right triangle $A B C$ with $C = 90^{\circ}$ , $B = 37^{\circ}$ , $c = 24$ . Round sides to the nearest tenth. $A = 53^{\circ}$ , $a \approx 19.2$ , $b \approx 14.4$

How to do these

A right triangle has legs $7$ and $10$ . Find the angle opposite the side of length $7$ , to the nearest degree

The two legs are opposite and adjacent, so it is tangent: tan x = 7/10.
x = tan⁻¹(0.7), which is 34.99 on the calculator.

The answer is $35^{\circ}$ .

Where students go wrong

Pressing tan when the question needs tan⁻¹. tan takes an angle and gives a ratio; to get the angle back from the ratio it has to be the inverse. Also check the calculator is in degree mode, or every answer comes out wrong.

Also called finding missing angles or inverse trig ratios.

What you can put on this worksheet

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 → $33^{\circ}$
The acute angles, exactly: A right triangle has legs $6$ and $6 \sqrt{3}$ . Find the larger acute angle. → $60^{\circ}$
Solve the whole triangle: Solve right triangle $A B C$ with $C = 90^{\circ}$ , $B = 47^{\circ}$ , $b = 24$ . Round sides to the nearest tenth. → $A = 43^{\circ}$ , $a \approx 22.4$ , $c \approx 32.8$
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 → ${28.1}^{\circ}$
Triangles drawn any way round: How long is the leg marked $x$ ? Give it to the nearest tenth. — a right triangle, labeled 39, x, 48°, D, E, F → $29.0$
The altitude splits it into two right triangles: Find the length marked $x$ to the nearest tenth. — a triangle split into two right triangles by its altitude, labeled x, 26, 33°, 52° → $18.0$

Questions about these worksheets

Yes. Every solving right triangles 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.

Geometry is usually taken around 9th or 10th 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 solving right triangles 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 7: a missing side, any angle, rounded, an angle from two sides, with inverse trig, the acute angles, exactly, solve the whole triangle, all three sides given: find the angle, triangles drawn any way round and the altitude splits it into two right triangles. Tick as many as you want and set how many of each, or let it spread them evenly.

Solving right triangles worksheet for Geometry

Select your difficulty

Find the missing side

Find the missing angle

Find an acute angle exactly

Solve the right triangle

Find the missing side

Find the missing angle

Find an acute angle exactly

Solve the right triangle

How to do these

Where students go wrong

What you can put on this worksheet

Questions about these worksheets

Are these solving right triangles worksheets free?+

Do the solving right triangles worksheets come with an answer key?+

Are these solving right triangles worksheets printable?+

What grade are these solving right triangles worksheets for?+

Can I get a different version of the same solving right triangles worksheet?+

Is this a free alternative to Kuta Software for solving right triangles?+

Can I choose how hard the solving right triangles questions are?+

What kinds of question are on a solving right triangles worksheet?+

What do students get wrong with solving right triangles?+