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Worksheet: Finding a Missing Angle in a Right Triangle Using Inverse Trigonometric Functions

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 meters and the length is 20 meters. Find the measure of giving the answer to two decimal places.

  • A
  • B
  • C
  • D

Q2:

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

  • A
  • B
  • C
  • D

Q3:

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

  • A
  • B
  • C
  • D

Q4:

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

Q5:

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

Q6:

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

Q7:

For the given figure, find the measure of ∠ 𝐵 𝐴 𝐶 , in degrees, to two decimal places.

Q8:

For the given figure, find the measure of ∠ 𝐵 𝐴 𝐶 , in degrees, to two decimal places.

Q9:

For the given figure, find the measures of ∠ 𝐴 𝐶 𝐵 and ∠ 𝐵 𝐴 𝐶 , in degrees, to two decimal places.

  • A ∠ 𝐴 𝐶 𝐵 = 3 7 . 9 9 ∘ , ∠ 𝐵 𝐴 𝐶 = 5 2 . 0 1 ∘
  • B ∠ 𝐴 𝐶 𝐵 = 3 6 . 8 7 ∘ , ∠ 𝐵 𝐴 𝐶 = 5 3 . 1 3 ∘
  • C ∠ 𝐴 𝐶 𝐵 = 5 1 . 3 4 ∘ , ∠ 𝐵 𝐴 𝐶 = 3 8 . 6 6 ∘
  • D ∠ 𝐴 𝐶 𝐵 = 3 8 . 6 6 ∘ , ∠ 𝐵 𝐴 𝐶 = 5 1 . 3 4 ∘
  • E ∠ 𝐴 𝐶 𝐵 = 5 3 . 1 3 ∘ , ∠ 𝐵 𝐴 𝐶 = 3 6 . 8 7 ∘

Q10:

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

Q11:

For the given figure, find the measures of ∠ 𝐴 𝐵 𝐶 and ∠ 𝐴 𝐶 𝐵 , in degrees, to two decimal places.

  • A 𝑚 ∠ 𝐴 𝐵 𝐶 = 6 6 . 0 3 ∘ , 𝑚 ∠ 𝐴 𝐶 𝐵 = 2 3 . 9 6 ∘
  • B 𝑚 ∠ 𝐴 𝐵 𝐶 = 2 6 . 3 9 ∘ , 𝑚 ∠ 𝐴 𝐶 𝐵 = 6 3 . 6 1 ∘
  • C 𝑚 ∠ 𝐴 𝐵 𝐶 = 6 3 . 4 3 ∘ , 𝑚 ∠ 𝐴 𝐶 𝐵 = 2 6 . 5 7 ∘
  • D 𝑚 ∠ 𝐴 𝐵 𝐶 = 6 3 . 6 1 ∘ , 𝑚 ∠ 𝐴 𝐶 𝐵 = 2 6 . 3 9 ∘
  • E 𝑚 ∠ 𝐴 𝐵 𝐶 = 2 6 . 5 7 ∘ , 𝑚 ∠ 𝐴 𝐶 𝐵 = 6 3 . 4 3 ∘

Q12:

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 ∘

Q13:

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 ∘

Q14:

𝐴 𝐵 𝐶 is a right-angled triangle at 𝐵 where 𝐵 𝐶 = 1 0 . 7 c m and 𝐴 𝐶 = 2 0 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 7 c m , 𝑚 ∠ 𝐴 = 4 3 ∘ , 𝑚 ∠ 𝐶 = 4 7 ∘
  • B 𝐴 𝐵 = 1 7 c m , 𝑚 ∠ 𝐴 = 3 3 ∘ , 𝑚 ∠ 𝐶 = 5 7 ∘
  • C 𝐴 𝐵 = 1 7 c m , 𝑚 ∠ 𝐴 = 4 4 ∘ , 𝑚 ∠ 𝐶 = 4 6 ∘
  • D 𝐴 𝐵 = 1 7 c m , 𝑚 ∠ 𝐴 = 3 2 ∘ , 𝑚 ∠ 𝐶 = 5 8 ∘

Q15:

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

  • A 𝐴 𝐵 = 9 . 3 2 , 𝐵 𝐶 = 1 1 . 0 8 , 𝑚 ∠ 𝐴 𝐵 𝐶 = 3 7 . 0 0 ∘
  • B 𝐴 𝐵 = 5 . 0 9 , 𝐵 𝐶 = 7 . 8 6 , 𝑚 ∠ 𝐴 𝐵 𝐶 = 3 2 . 0 0 ∘
  • C 𝐴 𝐵 = 8 . 7 0 , 𝐵 𝐶 = 1 0 . 5 7 , 𝑚 ∠ 𝐴 𝐵 𝐶 = 3 2 . 0 0 ∘
  • D 𝐴 𝐵 = 9 . 6 0 , 𝐵 𝐶 = 1 1 . 3 2 , 𝑚 ∠ 𝐴 𝐵 𝐶 = 3 2 . 0 0 ∘
  • E 𝐴 𝐵 = 9 . 8 8 , 𝐵 𝐶 = 1 1 . 5 6 , 𝑚 ∠ 𝐴 𝐵 𝐶 = 3 5 . 0 0 ∘

Q16:

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

  • A 𝐴 𝐶 = 1 0 . 3 4 , 𝐵 𝐶 = 9 . 5 3 , 𝑚 ∠ 𝐵 𝐴 𝐶 = 7 0 . 0 0 ∘
  • B 𝐴 𝐶 = 1 0 . 5 7 , 𝐵 𝐶 = 9 . 7 8 , 𝑚 ∠ 𝐵 𝐴 𝐶 = 6 8 . 0 0 ∘
  • C 𝐴 𝐶 = 1 0 . 6 8 , 𝐵 𝐶 = 9 . 9 0 , 𝑚 ∠ 𝐵 𝐴 𝐶 = 6 9 . 0 0 ∘
  • D 𝐴 𝐶 = 1 0 . 6 8 , 𝐵 𝐶 = 9 . 9 0 , 𝑚 ∠ 𝐵 𝐴 𝐶 = 6 8 . 0 0 ∘
  • E 𝐴 𝐶 = 1 0 . 2 3 , 𝐵 𝐶 = 9 . 4 2 , 𝑚 ∠ 𝐵 𝐴 𝐶 = 6 8 . 0 0 ∘

Q17:

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

  • A 𝐴 𝐶 = 7 . 6 2 , 𝐵 𝐶 = 8 . 1 9 , 𝑚 ∠ 𝐴 𝐵 𝐶 = 7 0 . 0 0 ∘
  • B 𝐴 𝐶 = 7 . 3 2 , 𝐵 𝐶 = 7 . 9 1 , 𝑚 ∠ 𝐴 𝐵 𝐶 = 7 2 . 0 0 ∘
  • C 𝐴 𝐶 = 7 . 9 5 , 𝐵 𝐶 = 8 . 1 9 , 𝑚 ∠ 𝐴 𝐵 𝐶 = 6 0 . 0 0 ∘
  • D 𝐴 𝐶 = 7 . 8 2 , 𝐵 𝐶 = 8 . 3 7 , 𝑚 ∠ 𝐴 𝐵 𝐶 = 6 9 . 0 0 ∘
  • E 𝐴 𝐶 = 7 . 2 2 , 𝐵 𝐶 = 7 . 8 2 , 𝑚 ∠ 𝐴 𝐵 𝐶 = 6 9 . 0 0 ∘

Q18:

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 ∘

Q19:

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

  • A 𝐴 𝐵 = 7 . 0 3 , 𝐴 𝐶 = 5 . 5 4 , 𝑚 ∠ 𝐵 𝐶 𝐴 = 5 3 . 0 0 ∘
  • B 𝐴 𝐵 = 7 . 0 3 , 𝐴 𝐶 = 5 . 5 4 , 𝑚 ∠ 𝐵 𝐶 𝐴 = 5 2 . 0 0 ∘
  • C 𝐴 𝐵 = 7 . 0 9 , 𝐴 𝐶 = 5 . 5 4 , 𝑚 ∠ 𝐵 𝐶 𝐴 = 5 3 . 0 0 ∘
  • D 𝐴 𝐵 = 7 . 0 9 , 𝐴 𝐶 = 5 . 5 4 , 𝑚 ∠ 𝐵 𝐶 𝐴 = 5 2 . 0 0 ∘
  • E 𝐴 𝐵 = 6 . 5 8 , 𝐴 𝐶 = 6 . 1 4 , 𝑚 ∠ 𝐵 𝐶 𝐴 = 5 2 . 0 0 ∘

Q20:

is a right-angled triangle at where and . Find the lengths of and giving the answers to two decimal places and the size of angle giving the answer to the nearest degree.

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

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