Solve right triangle ABC with C = 90°, A = 19°, a = 24. Round sides to the nearest tenth.

B = 71°, b is about 69.7, c is about 73.7

Solve right triangle ABC with C = 90°, A = 45°, c = 12. Round sides to the nearest tenth.

B = 45°, a is about 8.5, b is about 8.5

Solve right triangle ABC with C = 90°, A = 52°, b = 18. Round sides to the nearest tenth.

B = 38°, a is about 23.0, c is about 29.2

Solve right triangle ABC with C = 90°, A = 42°, b = 22. Round sides to the nearest tenth.

B = 48°, a is about 19.8, c is about 29.6

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

B = 43°, b is about 22.4, c is about 32.8

Worksheets · Precalculus

Precalculus solving right triangles worksheet

In Precalculus right triangles are the base for the trig functions, and the problems are mostly applications: angles of elevation and depression, heights and distances. Draw the picture and mark the right angle before choosing a ratio.

Also taught in Geometry and Algebra 2, 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 $x$ . Round to the nearest tenth. Find $θ$ . Round to the nearest degree. A right triangle has leg $13$ and hypotenuse $13 \sqrt{2}$ . Find the acute angles Solve right triangle $A B C$ with $C = 9 0^{\circ}$ , $A = 1 9^{\circ}$ , $a = 24$ . Round sides to the nearest tenth. Find $θ$ to the nearest tenth of a degree Find $x$ . Round to the nearest tenth. Find $θ$ . Round to the nearest degree. A right triangle has legs $15$ and $15 \sqrt{3}$ . Find the smaller acute angle Solve right triangle $A B C$ with $C = 9 0^{\circ}$ , $A = 4 5^{\circ}$ , $c = 12$ . Round sides to the nearest tenth. Find $θ$ to the nearest tenth of a degree Find $x$ . Round to the nearest tenth. Find $θ$ . Round to the nearest degree. A right triangle has legs $13$ and $13 \sqrt{3}$ . Find the larger acute angle Solve right triangle $A B C$ with $C = 9 0^{\circ}$ , $A = 5 2^{\circ}$ , $b = 18$ . Round sides to the nearest tenth. Find $θ$ to the nearest tenth of a degree Find $x$ . Round to the nearest tenth. Find $θ$ . Round to the nearest degree. A right triangle has legs $15$ and $15$ . Find the acute angles Solve right triangle $A B C$ with $C = 9 0^{\circ}$ , $A = 4 2^{\circ}$ , $b = 22$ . Round sides to the nearest tenth. 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

Solving Right Triangles

Date Period

Find each measure.

Find $x$ . Round to the nearest tenth.
Find $θ$ . Round to the nearest degree.
A right triangle has leg $13$ and hypotenuse $13 \sqrt{2}$ . Find the acute angles
Solve right triangle $A B C$ with $C = 9 0^{\circ}$ , $A = 1 9^{\circ}$ , $a = 24$ . Round sides to the nearest tenth.
Find $θ$ to the nearest tenth of a degree
Find $x$ . Round to the nearest tenth.
Find $θ$ . Round to the nearest degree.
A right triangle has legs $15$ and $15 \sqrt{3}$ . Find the smaller acute angle
Solve right triangle $A B C$ with $C = 9 0^{\circ}$ , $A = 4 5^{\circ}$ , $c = 12$ . Round sides to the nearest tenth.
Find $θ$ to the nearest tenth of a degree
Find $x$ . Round to the nearest tenth.
Find $θ$ . Round to the nearest degree.
A right triangle has legs $13$ and $13 \sqrt{3}$ . Find the larger acute angle
Solve right triangle $A B C$ with $C = 9 0^{\circ}$ , $A = 5 2^{\circ}$ , $b = 18$ . Round sides to the nearest tenth.
Find $θ$ to the nearest tenth of a degree
Find $x$ . Round to the nearest tenth.
Find $θ$ . Round to the nearest degree.
A right triangle has legs $15$ and $15$ . Find the acute angles
Solve right triangle $A B C$ with $C = 9 0^{\circ}$ , $A = 4 2^{\circ}$ , $b = 22$ . Round sides to the nearest tenth.
Find $θ$ to the nearest tenth of a degree



Sigma Prep · sigmaprep.io/worksheets Name Solving Right TrianglesAnswer keyVersion 1 Date Period Find each measure. Find $x$ . Round to the nearest tenth. $10.3$ Find $θ$ . Round to the nearest degree. $4 3^{\circ}$ A right triangle has leg $13$ and hypotenuse $13 \sqrt{2}$ . Find the acute angles $4 5^{\circ}$ and $4 5^{\circ}$ Solve right triangle $A B C$ with $C = 9 0^{\circ}$ , $A = 1 9^{\circ}$ , $a = 24$ . Round sides to the nearest tenth. $B = 7 1^{\circ}$ , $b \approx 69.7$ , $c \approx 73.7$ Find $θ$ to the nearest tenth of a degree $61.9$ Find $x$ . Round to the nearest tenth. $43.2$ Find $θ$ . Round to the nearest degree. $3 1^{\circ}$ A right triangle has legs $15$ and $15 \sqrt{3}$ . Find the smaller acute angle $3 0^{\circ}$ Solve right triangle $A B C$ with $C = 9 0^{\circ}$ , $A = 4 5^{\circ}$ , $c = 12$ . Round sides to the nearest tenth. $B = 4 5^{\circ}$ , $a \approx 8.5$ , $b \approx 8.5$ Find $θ$ to the nearest tenth of a degree $48.9$ Find $x$ . Round to the nearest tenth. $43.3$ Find $θ$ . Round to the nearest degree. $6 9^{\circ}$ A right triangle has legs $13$ and $13 \sqrt{3}$ . Find the larger acute angle $6 0^{\circ}$ Solve right triangle $A B C$ with $C = 9 0^{\circ}$ , $A = 5 2^{\circ}$ , $b = 18$ . Round sides to the nearest tenth. $B = 3 8^{\circ}$ , $a \approx 23.0$ , $c \approx 29.2$ Find $θ$ to the nearest tenth of a degree $36.9$ Find $x$ . Round to the nearest tenth. $12.5$ Find $θ$ . Round to the nearest degree. $2 6^{\circ}$ A right triangle has legs $15$ and $15$ . Find the acute angles $4 5^{\circ}$ and $4 5^{\circ}$ Solve right triangle $A B C$ with $C = 9 0^{\circ}$ , $A = 4 2^{\circ}$ , $b = 22$ . Round sides to the nearest tenth. $B = 4 8^{\circ}$ , $a \approx 19.8$ , $c \approx 29.6$ Find $θ$ to the nearest tenth of a degree $59.5$ 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 $x$ . Round to the nearest tenth. $10.3$
Find $θ$ . Round to the nearest degree. $4 3^{\circ}$
A right triangle has leg $13$ and hypotenuse $13 \sqrt{2}$ . Find the acute angles $4 5^{\circ}$ and $4 5^{\circ}$
Solve right triangle $A B C$ with $C = 9 0^{\circ}$ , $A = 1 9^{\circ}$ , $a = 24$ . Round sides to the nearest tenth. $B = 7 1^{\circ}$ , $b \approx 69.7$ , $c \approx 73.7$
Find $θ$ to the nearest tenth of a degree $61.9$
Find $x$ . Round to the nearest tenth. $43.2$
Find $θ$ . Round to the nearest degree. $3 1^{\circ}$
A right triangle has legs $15$ and $15 \sqrt{3}$ . Find the smaller acute angle $3 0^{\circ}$
Solve right triangle $A B C$ with $C = 9 0^{\circ}$ , $A = 4 5^{\circ}$ , $c = 12$ . Round sides to the nearest tenth. $B = 4 5^{\circ}$ , $a \approx 8.5$ , $b \approx 8.5$
Find $θ$ to the nearest tenth of a degree $48.9$
Find $x$ . Round to the nearest tenth. $43.3$
Find $θ$ . Round to the nearest degree. $6 9^{\circ}$
A right triangle has legs $13$ and $13 \sqrt{3}$ . Find the larger acute angle $6 0^{\circ}$
Solve right triangle $A B C$ with $C = 9 0^{\circ}$ , $A = 5 2^{\circ}$ , $b = 18$ . Round sides to the nearest tenth. $B = 3 8^{\circ}$ , $a \approx 23.0$ , $c \approx 29.2$
Find $θ$ to the nearest tenth of a degree $36.9$
Find $x$ . Round to the nearest tenth. $12.5$
Find $θ$ . Round to the nearest degree. $2 6^{\circ}$
A right triangle has legs $15$ and $15$ . Find the acute angles $4 5^{\circ}$ and $4 5^{\circ}$
Solve right triangle $A B C$ with $C = 9 0^{\circ}$ , $A = 4 2^{\circ}$ , $b = 22$ . Round sides to the nearest tenth. $B = 4 8^{\circ}$ , $a \approx 19.8$ , $c \approx 29.6$
Find $θ$ to the nearest tenth of a degree $59.5$

How to do these

From 50 m away, the angle of elevation to the top of a tower is $3 8^{\circ}$ . Find its height

The 50 m is adjacent to the angle and the height is opposite, so use tangent.
h = 50 tan 38°.
50 × 0.7813 = 39.06.

The answer is $h \approx 39.1$ m.

Where students go wrong

Measuring an angle of depression from the vertical. It is measured down from the horizontal, so it equals the angle of elevation from the other end.

Also called finding missing angles or inverse trig ratios.

What you can put on this worksheet

A missing side, any angle, rounded: Find $x$ . Round 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 → $3 3^{\circ}$
The acute angles, exactly: A right triangle has legs $6$ and $6 \sqrt{3}$ . Find the larger acute angle → $6 0^{\circ}$
Solve the whole triangle: Solve right triangle $A B C$ with $C = 9 0^{\circ}$ , $A = 4 7^{\circ}$ , $a = 24$ . Round sides to the nearest tenth. → $B = 4 3^{\circ}$ , $b \approx 22.4$ , $c \approx 32.8$
All three sides given: find the angle: Find $θ$ to the nearest tenth of a degree — a right triangle with base 63, height 60 and hypotenuse 87 → $43.6$
Triangles drawn any way round: Find $x$ 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 $x$ to the nearest tenth — a triangle split into two right triangles by its altitude, labeled x, 32, 54°, 55° → $31.6$

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.

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 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.

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.

Precalculus solving right triangles worksheet

Select your difficulty

Solving Right Triangles

Solving Right TrianglesAnswer keyVersion 1

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?+

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Are these solving right triangles worksheets printable?+

What grade are these solving right triangles worksheets for?+

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