Trigonometry Right Triangles Worksheet

Question 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.

Accepted Answer

The opposite side is about 6.9 units because sin(35 degrees) = opposite over 12, so opposite = 12 × sin(35 degrees) ≈ 6.9.

Question 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.

Accepted Answer

The adjacent side is about 10.0 units because cos(48 degrees) = adjacent over 15, so adjacent = 15 × cos(48 degrees) ≈ 10.0.

Question 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.

Accepted Answer

The opposite side is about 4.8 units because tan(28 degrees) = opposite over 9, so opposite = 9 × tan(28 degrees) ≈ 4.8.

Question 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?

Accepted Answer

The ladder reaches about 18.8 feet up the wall because sin(70 degrees) = height over 20, so height = 20 × sin(70 degrees) ≈ 18.8.

Question 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.

Accepted Answer

The ramp is about 12.0 meters long because sin(12 degrees) = 2.5 over ramp length, so ramp length = 2.5 ÷ sin(12 degrees) ≈ 12.0.

Question 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.

Accepted Answer

The tree is about 12.2 meters tall because tan(41 degrees) = height over 14, so height = 14 × tan(41 degrees) ≈ 12.2.

Question 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.

Accepted Answer

Angle D is about 33 degrees because sin(D) = 7 over 13, so D = sin^-1(7/13) ≈ 32.6 degrees, which rounds to 33 degrees.

Question 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.

Accepted Answer

Angle E is about 50 degrees because cos(E) = 11 over 17, so E = cos^-1(11/17) ≈ 49.7 degrees, which rounds to 50 degrees.

Question 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.

Accepted Answer

Angle F is about 53 degrees because tan(F) = 8 over 6, so F = tan^-1(8/6) ≈ 53.1 degrees, which rounds to 53 degrees.

Question 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.

Accepted Answer

The horizontal distance is about 18.5 meters because cos(52 degrees) = distance over 30, so distance = 30 × cos(52 degrees) ≈ 18.5.

Question 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.

Accepted Answer

The vertical rise is about 2.8 feet because sin(9 degrees) = rise over 18, so rise = 18 × sin(9 degrees) ≈ 2.8.

Question 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.

Accepted Answer

The building is about 49.1 meters tall because tan(63 degrees) = height over 25, so height = 25 × tan(63 degrees) ≈ 49.1.

Question 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.

Accepted Answer

The adjacent side is about 20.1 centimeters because cos(24 degrees) = adjacent over 22, so adjacent = 22 × cos(24 degrees) ≈ 20.1.

Question 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.

Accepted Answer

The angle is about 23 degrees because tan(theta) = 5 over 12, so theta = tan^-1(5/12) ≈ 22.6 degrees, which rounds to 23 degrees.

Question 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.

Accepted Answer

The hill is about 20.4 yards above the surveyor because tan(27 degrees) = height over 40, so height = 40 × tan(27 degrees) ≈ 20.4.

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Trigonometry Right Triangles

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