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Lesson: Inverse Trigonometric Functions

In this lesson, we will learn how to find a missing angle in a right triangle using the appropriate inverse trigonometric function given two side lengths.

Sample Question Videos

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Worksheet • 19 Questions • 7 Videos

Q1:

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

Q2:

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

Q3:

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

Q4:

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

  • A
  • B
  • C
  • D
  • E

Q5:

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

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 sizes of and , in degrees, to two decimal places.

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

Q8:

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 , ,

Q9:

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 , ,

Q10:

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

  • A 𝐴 𝐡 = 1 5 c m , π‘š ∠ 𝐴 = 3 4 ∘ , π‘š ∠ 𝐢 = 5 6 ∘
  • B 𝐴 𝐡 = 1 5 c m , π‘š ∠ 𝐴 = 3 5 ∘ , π‘š ∠ 𝐢 = 5 5 ∘
  • C 𝐴 𝐡 = 1 5 c m , π‘š ∠ 𝐴 = 4 3 ∘ , π‘š ∠ 𝐢 = 4 7 ∘
  • D 𝐴 𝐡 = 1 5 c m , π‘š ∠ 𝐴 = 4 2 ∘ , π‘š ∠ 𝐢 = 4 8 ∘

Q11:

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

  • A 𝐴 𝐡 = 1 5 c m , π‘š ∠ 𝐴 = 3 6 ∘ , π‘š ∠ 𝐢 = 5 4 ∘
  • B 𝐴 𝐡 = 1 5 c m , π‘š ∠ 𝐴 = 3 7 ∘ , π‘š ∠ 𝐢 = 5 3 ∘
  • C 𝐴 𝐡 = 1 5 c m , π‘š ∠ 𝐴 = 4 2 ∘ , π‘š ∠ 𝐢 = 4 8 ∘
  • D 𝐴 𝐡 = 1 5 c m , π‘š ∠ 𝐴 = 4 1 ∘ , π‘š ∠ 𝐢 = 4 9 ∘

Q12:

𝐴 𝐡 𝐢 is a right-angled triangle at 𝐡 where 𝐡 𝐢 = 1 0 . 7 c m and 𝐴 𝐢 = 2 0 c m . Find the length 𝐴 𝐡 , giving the answer to the nearest centimetre, and the measure of angles 𝐴 and 𝐢 , giving the answer to the nearest degree.

  • A 𝐴 𝐡 = 1 7 c m , π‘š ∠ 𝐴 = 3 2 ∘ , π‘š ∠ 𝐢 = 5 8 ∘
  • B 𝐴 𝐡 = 1 7 c m , π‘š ∠ 𝐴 = 3 3 ∘ , π‘š ∠ 𝐢 = 5 7 ∘
  • C 𝐴 𝐡 = 1 7 c m , π‘š ∠ 𝐴 = 4 4 ∘ , π‘š ∠ 𝐢 = 4 6 ∘
  • D 𝐴 𝐡 = 1 7 c m , π‘š ∠ 𝐴 = 4 3 ∘ , π‘š ∠ 𝐢 = 4 7 ∘

Q13:

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

  • A 𝐴 𝐡 = 9 . 2 4 , 𝐡 𝐢 = 1 1 . 0 2 , π‘š ∠ 𝐴 𝐢 𝐡 = 5 7 . 0 0 ∘
  • B 𝐴 𝐡 = 9 . 2 4 , 𝐡 𝐢 = 1 1 . 0 2 , π‘š ∠ 𝐴 𝐢 𝐡 = 5 6 . 0 0 ∘
  • C 𝐴 𝐡 = 4 . 8 2 , 𝐡 𝐢 = 1 0 . 4 2 , π‘š ∠ 𝐴 𝐢 𝐡 = 5 7 . 0 0 ∘
  • D 𝐴 𝐡 = 1 0 . 8 7 , 𝐡 𝐢 = 1 2 . 4 2 , π‘š ∠ 𝐴 𝐢 𝐡 = 5 7 . 0 0 ∘
  • E 𝐴 𝐡 = 1 0 . 8 7 , 𝐡 𝐢 = 1 2 . 4 2 , π‘š ∠ 𝐴 𝐢 𝐡 = 6 0 . 0 0 ∘

Q14:

For the given figure, find angle πœƒ , in degrees, to two decimal places.

Q15:

𝐴 𝐡 𝐢 is a right-angled triangle at 𝐡 where 𝐡 𝐢 = 2 5 c m and π‘š ∠ 𝐴 = 5 8 ∘ . Find the lengths of 𝐴 𝐢 and 𝐴 𝐡 .

  • A 𝐴 𝐢 = 2 9 . 4 8 c m , 𝐴 𝐡 = 1 5 . 6 2 c m , π‘š ∠ 𝐢 = 3 2 ∘
  • B 𝐴 𝐢 = 1 5 . 6 2 c m , 𝐴 𝐡 = 2 9 . 4 8 c m , π‘š ∠ 𝐢 = 3 2 ∘
  • C 𝐴 𝐢 = 1 5 . 6 2 c m , 𝐴 𝐡 = 2 9 . 4 8 c m , π‘š ∠ 𝐢 = 4 2 ∘
  • D 𝐴 𝐢 = 2 9 . 4 8 c m , 𝐴 𝐡 = 1 5 . 6 2 c m , π‘š ∠ 𝐢 = 4 2 ∘

Q16:

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 , ,

Q17:

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

  • A
  • B
  • C
  • D
  • E

Q18:

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

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

Q19:

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

  • A
  • B
  • C
  • D
  • E
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