Worksheet: Applications of Inverse Trigonometric Functions in a Right Triangle

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In this worksheet, we will practice finding a missing angle in a right triangle using the appropriate inverse trigonometric function given two side lengths.

Q1:

The height of a ski slope is 16 metres and the length is 20 metres. Find the measure of ∠ 𝜃 giving the answer to two decimal places.

Q2:

For the given figure, find the size of angle , in degrees, to two decimal places.

  • A
  • B
  • C
  • D
  • E

Q3:

In the given figure, find the measure of angle 𝜃 , in degrees, to two decimal places.

Q4:

Given the following figure, find the lengths of and and the size of in degrees. Give your answers to two decimal places.

  • A , ,
  • B , ,
  • C , ,
  • D , ,
  • E , ,

Q5:

Given the following figure, find the lengths of and and the size of in degrees. Give your answers to two decimal places.

  • A , ,
  • B , ,
  • C , ,
  • D , ,
  • E , ,

Q6:

For the given figure, find the size of , in degrees, to two decimal places.

  • A
  • B
  • C
  • D
  • E

Q7:

For the given figure, find the size of , in degrees, to two decimal places.

  • A
  • B
  • C
  • D
  • E

Q8:

Find the size of angle , in degrees, to two decimal places.

  • A
  • B
  • C
  • D
  • E

Q9:

For the given figure, find the sizes of and , in degrees, to two decimal places.

  • A ,
  • B ,
  • C ,
  • D ,
  • E ,

Q10:

Given the following figure, find the lengths of 𝐴 𝐵 and 𝐵 𝐶 and the measure of ∠ 𝐴 𝐶 𝐵 in degrees. Give your answers to two decimal places.

  • A 𝐴 𝐵 = 1 0 . 8 7 , 𝐵 𝐶 = 1 2 . 4 2 , 𝑚 ∠ 𝐴 𝐶 𝐵 = 6 0 . 0 0 ∘
  • B 𝐴 𝐵 = 4 . 8 2 , 𝐵 𝐶 = 1 0 . 4 2 , 𝑚 ∠ 𝐴 𝐶 𝐵 = 5 7 . 0 0 ∘
  • C 𝐴 𝐵 = 1 0 . 8 7 , 𝐵 𝐶 = 1 2 . 4 2 , 𝑚 ∠ 𝐴 𝐶 𝐵 = 5 7 . 0 0 ∘
  • D 𝐴 𝐵 = 9 . 2 4 , 𝐵 𝐶 = 1 1 . 0 2 , 𝑚 ∠ 𝐴 𝐶 𝐵 = 5 7 . 0 0 ∘
  • E 𝐴 𝐵 = 9 . 2 4 , 𝐵 𝐶 = 1 1 . 0 2 , 𝑚 ∠ 𝐴 𝐶 𝐵 = 5 6 . 0 0 ∘

Q11:

Given the following figure, find the lengths of and and the size of in degrees. Give your answers to two decimal places.

  • A , ,
  • B , ,
  • C , ,
  • D , ,
  • E , ,

Q12:

𝐴 𝐵 𝐶 is a right-angled triangle at 𝐵 where 𝐵 𝐶 = 2 5 c m and 𝑚 ∠ 𝐴 = 5 8 ∘ . Find the lengths of 𝐴 𝐶 and 𝐴 𝐵 and the measure of ∠ 𝐶 .

  • A 𝐴 𝐶 = 2 9 . 4 8 c m , 𝐴 𝐵 = 1 5 . 6 2 c m , 𝑚 ∠ 𝐶 = 4 2 ∘
  • B 𝐴 𝐶 = 1 5 . 6 2 c m , 𝐴 𝐵 = 2 9 . 4 8 c m , 𝑚 ∠ 𝐶 = 3 2 ∘
  • C 𝐴 𝐶 = 1 5 . 6 2 c m , 𝐴 𝐵 = 2 9 . 4 8 c m , 𝑚 ∠ 𝐶 = 4 2 ∘
  • D 𝐴 𝐶 = 2 9 . 4 8 c m , 𝐴 𝐵 = 1 5 . 6 2 c m , 𝑚 ∠ 𝐶 = 3 2 ∘

Q13:

For the given figure, find angle 𝜃 , in degrees, to two decimal places.

Q14:

For the given figure, find the sizes of and , in degrees, to two decimal places.

  • A ,
  • B ,
  • C ,
  • D ,
  • E ,

Q15:

𝐴 𝐵 𝐶 is a right-angled triangle at 𝐵 where 𝐵 𝐶 = 1 0 c m and 𝐴 𝐶 = 1 8 c m . Find the length 𝐴 𝐵 , giving the answer to the nearest centimetre, and the measure of angles 𝐴 and 𝐶 , giving the answer to the nearest degree.

  • A 𝐴 𝐵 = 1 5 c m , 𝑚 ∠ 𝐴 = 4 2 ∘ , 𝑚 ∠ 𝐶 = 4 8 ∘
  • B 𝐴 𝐵 = 1 5 c m , 𝑚 ∠ 𝐴 = 3 5 ∘ , 𝑚 ∠ 𝐶 = 5 5 ∘
  • C 𝐴 𝐵 = 1 5 c m , 𝑚 ∠ 𝐴 = 4 3 ∘ , 𝑚 ∠ 𝐶 = 4 7 ∘
  • D 𝐴 𝐵 = 1 5 c m , 𝑚 ∠ 𝐴 = 3 4 ∘ , 𝑚 ∠ 𝐶 = 5 6 ∘

Q16:

James leans a 5 m ladder against a wall that is perpendicular to the ground. He positions the ladder such that the angle between the base of the ladder and the ground is 7 2 ∘ . Determine the height, ℎ , at which the top of the ladder touches the wall, the angle between the top of the ladder and the wall, 𝜃 , and the distance, 𝑑 , between the bottom of the ladder and the base of the wall. If necessary, round your answers to two decimal places.

  • A ℎ = 5 . 2 6 m, 𝜃 = 1 8 ∘ , 𝑑 = 1 . 5 5 m
  • B ℎ = 1 . 5 5 m, 𝜃 = 1 8 ∘ , 𝑑 = 4 . 7 6 m
  • C ℎ = 4 . 7 6 m, 𝜃 = 5 7 ∘ , 𝑑 = 1 . 5 5 m
  • D ℎ = 4 . 7 6 m, 𝜃 = 1 8 ∘ , 𝑑 = 1 . 5 5 m
  • E ℎ = 1 . 5 5 m, 𝜃 = 5 7 ∘ , 𝑑 = 4 . 7 6 m

Q17:

The height of a ski slope is 4 metres and the length is 5 metres. Find the measure of ∠ 𝜃 giving the answer to two decimal places.

Q18:

The height of a ski slope is 3 metres and the length is 5 metres. Find the measure of ∠ 𝜃 giving the answer to two decimal places.

Q19:

𝐴 𝐵 𝐶 is a right-angled triangle at 𝐵 where 𝐵 𝐶 = 1 1 . 3 c m and 𝐴 𝐶 = 1 9 c m . Find the length 𝐴 𝐵 , giving the answer to the nearest centimetre, and the measure of angles 𝐴 and 𝐶 , giving the answer to the nearest degree.

  • A 𝐴 𝐵 = 1 5 c m , 𝑚 ∠ 𝐴 = 4 1 ∘ , 𝑚 ∠ 𝐶 = 4 9 ∘
  • B 𝐴 𝐵 = 1 5 c m , 𝑚 ∠ 𝐴 = 3 7 ∘ , 𝑚 ∠ 𝐶 = 5 3 ∘
  • C 𝐴 𝐵 = 1 5 c m , 𝑚 ∠ 𝐴 = 4 2 ∘ , 𝑚 ∠ 𝐶 = 4 8 ∘
  • D 𝐴 𝐵 = 1 5 c m , 𝑚 ∠ 𝐴 = 3 6 ∘ , 𝑚 ∠ 𝐶 = 5 4 ∘

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