Practice identifying opposite, adjacent, and hypotenuse sides and using sine, cosine, and tangent to solve right triangle problems.
Read each problem carefully. Round decimal answers to the nearest tenth unless the problem says otherwise. Show your work in the space provided.
Practice using sine, cosine, and tangent in right triangles
Geometry - Grade 9-12
- 1
In a right triangle, angle A is an acute angle. The side opposite angle A is 7, the side adjacent to angle A is 24, and the hypotenuse is 25. Write sin A, cos A, and tan A as fractions.
- 2
A right triangle has an acute angle of 35 degrees. The hypotenuse is 18 cm. Which trig ratio should you use to find the side opposite the 35 degree angle, and what is the length of that side?
- 3
A right triangle has an acute angle of 62 degrees. The side adjacent to the angle is 9 inches. Find the hypotenuse.
- 4
A ladder leans against a wall and makes a 70 degree angle with the ground. The ladder is 15 feet long. How high up the wall does the ladder reach?
- 5
A ramp rises 4 feet over a horizontal distance of 12 feet. What is the angle of elevation of the ramp to the nearest degree?
- 6
For an acute angle B in a right triangle, sin B = 5/13. If the hypotenuse is 26 units, find the side opposite angle B.
- 7
A right triangle has an acute angle of 48 degrees and an adjacent side of 14 meters. Find the length of the opposite side.
- 8
A cable is attached from the top of a pole to a point on the ground 20 feet from the base of the pole. The cable makes a 38 degree angle with the ground. How tall is the pole?
- 9
In a right triangle, angle C is acute. The opposite side is 16 and the adjacent side is 30. Find angle C to the nearest degree.
- 10
A right triangle has an acute angle of 25 degrees and a hypotenuse of 40 centimeters. Find the side adjacent to the 25 degree angle.
- 11
A boat is 85 meters from the base of a lighthouse. The angle of elevation from the boat to the top of the lighthouse is 12 degrees. Find the height of the lighthouse.
- 12
A right triangle has legs of 8 and 15 and a hypotenuse of 17. For the acute angle opposite the side of length 8, write the sine, cosine, and tangent ratios as fractions.