Geometry Right Triangle Trigonometry Worksheet (PDF)

Geometry math worksheet: Right Triangle Trigonometry – Maths PDF

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This right triangles worksheet for Geometry covers right triangle trigonometry (Common Core G-SRT.C.6, G-SRT.C.7, G-SRT.C.8), with a free PDF to print.

These 20 problems practice sine, cosine, tangent, complementary angles and solving right triangles (Common Core G-SRT.C.6 to G-SRT.C.8). The first problems are quick one-step checks of the definitions and formulas from the lesson. The middle problems ask for diagrams, equations and careful reasoning in the style of a high school Geometry class. The last six problems are applications with ladders, trees, ramps and lighthouses.

Geometry · Common Core State Standards: G-SRT.C.6, G-SRT.C.7, G-SRT.C.8

Right triangles worksheet: exercises 1 to 10

Exercise 1 – Name the ratios

Sides are named relative to angle A.

For the triangle with legs 3 and 4 and hypotenuse 5, write \(\text{sin}\,A\), \(\text{cos}\,A\) and \(\text{tan}\,A\) as fractions.

Exercise 2 – Sine of a 5-12-13 triangle

In a right triangle with legs 5 and 12 and hypotenuse 13, find \(\text{sin}\,A\) where A is opposite the leg of length 5.

Exercise 3 – Tangent

A right triangle has legs 8 and 15. Find the hypotenuse and the tangent of the angle opposite the leg of length 8.

Exercise 4 – Find a side with sine

Use a ratio that connects the known side and the unknown side.

In the right triangle the hypotenuse is 20 and angle A is \(35^{\circ}\). Find the side opposite A to the nearest tenth.

Exercise 5 – Find a side with cosine

The hypotenuse of a right triangle is 15 and an acute angle is \(52^{\circ}\). Find the side adjacent to that angle to the nearest tenth.

Exercise 6 – Find a side with tangent

Adjacent side 12.

An acute angle of a right triangle is \(28^{\circ}\) and the adjacent side is 12. Find the opposite side to the nearest tenth.

Exercise 7 – Find an angle: sine

Find the acute angle A if \(\text{sin}\,A = 0.6\). Round to the nearest tenth of a degree.

Exercise 8 – Find an angle from sides

Legs 7 and 24.

A right triangle has legs 7 and 24. Find the angle opposite the leg of length 7 to the nearest tenth.

Exercise 9 – Complementary angles

Find the missing angle: \(\text{sin}\,25^{\circ} = \text{cos}\,x^{\circ}\).

Exercise 10 – Check complementary

Use a calculator to check that \(\text{sin}\,38^{\circ}\) and \(\text{cos}\,52^{\circ}\) are equal to four decimal places.

Exercises 11 and up

Exercise 11 – Solve a right triangle

Legs 9 and 12.

Solve the right triangle with legs 9 and 12: find the hypotenuse and both acute angles to the nearest tenth.

Exercise 12 – Solve from hypotenuse and angle

A right triangle has hypotenuse 25 and an acute angle of \(40^{\circ}\). Find the other acute angle and both legs to the nearest tenth.

Exercise 13 – Solve from a leg and angle

A right triangle has a leg of 10 adjacent to a \(62^{\circ}\) angle. Find the opposite leg and the hypotenuse to the nearest tenth.

Exercise 14 – 30-60-90 triangle

30-60-90 triangle.

A 30-60-90 triangle has hypotenuse 14. Find the legs, using the fact that the side opposite 30° is half the hypotenuse.

Exercise 15 – 45-45-90 triangle

A 45-45-90 triangle has legs of 9. Find the hypotenuse in simplest radical form and as a decimal to the nearest hundredth.

Exercise 16 – Guy wire

A guy wire holding a pole.

A 30-foot guy wire runs from the top of a pole to an anchor in the ground and makes a \(62^{\circ}\) angle with the ground. How tall is the pole, and how far is the anchor from the base of the pole? Round to the nearest tenth.

Exercise 17 – Height of a windmill

Angle of elevation to the top of a windmill.

Mei stands 80 feet from the base of a windmill. The angle of elevation to the top of the tower is \(41^{\circ}\). Find the height of the tower to the nearest tenth. Ignore her eye height.

Exercise 18 – Wheelchair ramp

A ramp rises 2.5 feet over a horizontal run of 30 feet. Find the angle the ramp makes with the ground to the nearest tenth of a degree.

Exercise 19 – Lighthouse

From the top of a lighthouse 80 feet above the water, the angle of depression to a boat is \(12^{\circ}\). Find the horizontal distance from the boat to the base of the lighthouse to the nearest foot.

Exercise 20 – Kite string

A kite string is 120 feet long and makes a \(54^{\circ}\) angle with level ground. Assume the string is straight. Find the kite’s height above the ground to the nearest tenth of a foot.

Key facts behind this right triangles worksheet

Key facts

sin A = opposite/hypotenuse, cos A = adjacent/hypotenuse, tan A = opposite/adjacent.
sin A = cos (90 degrees minus A) for the acute angles of a right triangle.
Use an inverse function (sin^-1, cos^-1, tan^-1) to find an angle.
Solving a right triangle means finding all sides and acute angles.
Angles of elevation and depression are measured from the horizontal.

How to use this right triangles worksheet

Work through the exercises in order: they go from simple to challenging. Write every step on paper, then compare with the solutions page and redo any exercise you missed the next day.

Download the right triangles worksheet as a PDF with the button below and keep it with your notes.

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