Practice finding side lengths and angle measures in right triangles using sine, cosine, and tangent.
Read each problem carefully. Use the correct trigonometric ratio or inverse trigonometric function. Round decimal answers to the nearest tenth unless the problem says otherwise.
Using sine, cosine, and tangent in right triangles
Math - Grade 9-12
- 1
In a right triangle, angle A is 35 degrees and the hypotenuse is 12 units. Find the length of the side opposite angle A.
- 2
In a right triangle, angle B is 48 degrees and the hypotenuse is 15 units. Find the length of the side adjacent to angle B.
- 3
In a right triangle, angle C is 28 degrees and the side adjacent to angle C is 9 units. Find the length of the side opposite angle C.
- 4
A ladder leans against a wall, making a 70 degree angle with the ground. If the ladder is 20 feet long, how high up the wall does it reach?
- 5
A ramp makes a 12 degree angle with the ground and rises to a height of 2.5 meters. Find the length of the ramp.
- 6
A tree casts a shadow 14 meters long. The angle of elevation from the tip of the shadow to the top of the tree is 41 degrees. Find the height of the tree.
- 7
In a right triangle, the side opposite angle D is 7 units and the hypotenuse is 13 units. Find angle D to the nearest degree.
- 8
In a right triangle, the adjacent side to angle E is 11 units and the hypotenuse is 17 units. Find angle E to the nearest degree.
- 9
In a right triangle, the opposite side to angle F is 8 units and the adjacent side is 6 units. Find angle F to the nearest degree.
- 10
A kite string is 30 meters long and makes a 52 degree angle with the ground. Find the horizontal distance from the person holding the string to the point directly below the kite.
- 11
A wheelchair ramp is 18 feet long and makes an angle of 9 degrees with the ground. Find the vertical rise of the ramp.
- 12
From a point on the ground, the angle of elevation to the top of a building is 63 degrees. If the point is 25 meters from the base of the building, find the building's height.
- 13
In a right triangle, one acute angle measures 24 degrees and the hypotenuse is 22 centimeters. Find the side adjacent to the 24 degree angle.
- 14
In a right triangle, the side opposite an angle is 5 units and the adjacent side is 12 units. Find the angle to the nearest degree.
- 15
A surveyor stands 40 yards from the base of a hill. The angle of elevation to the top of the hill is 27 degrees. Find the height of the hill above the surveyor.