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

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 πœƒ , in degrees, to two decimal places.

Q5:

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

Q6:

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

Q7:

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

Q8:

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

Q9:

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

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

Q10:

Find the measure of angle πœƒ , in degrees, to two decimal places.

Q11:

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

  • A π‘š ∠ 𝐴 𝐡 𝐢 = 6 6 . 0 3 ∘ , π‘š ∠ 𝐴 𝐢 𝐡 = 2 3 . 9 6 ∘
  • B π‘š ∠ 𝐴 𝐡 𝐢 = 2 6 . 3 9 ∘ , π‘š ∠ 𝐴 𝐢 𝐡 = 6 3 . 6 1 ∘
  • C π‘š ∠ 𝐴 𝐡 𝐢 = 6 3 . 4 3 ∘ , π‘š ∠ 𝐴 𝐢 𝐡 = 2 6 . 5 7 ∘
  • D π‘š ∠ 𝐴 𝐡 𝐢 = 6 3 . 6 1 ∘ , π‘š ∠ 𝐴 𝐢 𝐡 = 2 6 . 3 9 ∘
  • E π‘š ∠ 𝐴 𝐡 𝐢 = 2 6 . 5 7 ∘ , π‘š ∠ 𝐴 𝐢 𝐡 = 6 3 . 4 3 ∘

Q12:

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 = 4 2 ∘ , π‘š ∠ 𝐢 = 4 8 ∘
  • 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 = 3 4 ∘ , π‘š ∠ 𝐢 = 5 6 ∘

Q13:

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 = 4 1 ∘ , π‘š ∠ 𝐢 = 4 9 ∘
  • 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 = 3 6 ∘ , π‘š ∠ 𝐢 = 5 4 ∘

Q14:

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 = 4 3 ∘ , π‘š ∠ 𝐢 = 4 7 ∘
  • 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 = 3 2 ∘ , π‘š ∠ 𝐢 = 5 8 ∘

Q15:

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

  • A 𝐴 𝐡 = 9 . 3 2 , 𝐡 𝐢 = 1 1 . 0 8 , π‘š ∠ 𝐴 𝐡 𝐢 = 3 7 . 0 0 ∘
  • B 𝐴 𝐡 = 5 . 0 9 , 𝐡 𝐢 = 7 . 8 6 , π‘š ∠ 𝐴 𝐡 𝐢 = 3 2 . 0 0 ∘
  • C 𝐴 𝐡 = 8 . 7 0 , 𝐡 𝐢 = 1 0 . 5 7 , π‘š ∠ 𝐴 𝐡 𝐢 = 3 2 . 0 0 ∘
  • D 𝐴 𝐡 = 9 . 6 0 , 𝐡 𝐢 = 1 1 . 3 2 , π‘š ∠ 𝐴 𝐡 𝐢 = 3 2 . 0 0 ∘
  • E 𝐴 𝐡 = 9 . 8 8 , 𝐡 𝐢 = 1 1 . 5 6 , π‘š ∠ 𝐴 𝐡 𝐢 = 3 5 . 0 0 ∘

Q16:

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

  • A 𝐴 𝐢 = 1 0 . 3 4 , 𝐡 𝐢 = 9 . 5 3 , π‘š ∠ 𝐡 𝐴 𝐢 = 7 0 . 0 0 ∘
  • B 𝐴 𝐢 = 1 0 . 5 7 , 𝐡 𝐢 = 9 . 7 8 , π‘š ∠ 𝐡 𝐴 𝐢 = 6 8 . 0 0 ∘
  • C 𝐴 𝐢 = 1 0 . 6 8 , 𝐡 𝐢 = 9 . 9 0 , π‘š ∠ 𝐡 𝐴 𝐢 = 6 9 . 0 0 ∘
  • D 𝐴 𝐢 = 1 0 . 6 8 , 𝐡 𝐢 = 9 . 9 0 , π‘š ∠ 𝐡 𝐴 𝐢 = 6 8 . 0 0 ∘
  • E 𝐴 𝐢 = 1 0 . 2 3 , 𝐡 𝐢 = 9 . 4 2 , π‘š ∠ 𝐡 𝐴 𝐢 = 6 8 . 0 0 ∘

Q17:

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

  • A 𝐴 𝐢 = 7 . 6 2 , 𝐡 𝐢 = 8 . 1 9 , π‘š ∠ 𝐴 𝐡 𝐢 = 7 0 . 0 0 ∘
  • B 𝐴 𝐢 = 7 . 3 2 , 𝐡 𝐢 = 7 . 9 1 , π‘š ∠ 𝐴 𝐡 𝐢 = 7 2 . 0 0 ∘
  • C 𝐴 𝐢 = 7 . 9 5 , 𝐡 𝐢 = 8 . 1 9 , π‘š ∠ 𝐴 𝐡 𝐢 = 6 0 . 0 0 ∘
  • D 𝐴 𝐢 = 7 . 8 2 , 𝐡 𝐢 = 8 . 3 7 , π‘š ∠ 𝐴 𝐡 𝐢 = 6 9 . 0 0 ∘
  • E 𝐴 𝐢 = 7 . 2 2 , 𝐡 𝐢 = 7 . 8 2 , π‘š ∠ 𝐴 𝐡 𝐢 = 6 9 . 0 0 ∘

Q18:

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

Q19:

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

  • A 𝐴 𝐡 = 7 . 0 3 , 𝐴 𝐢 = 5 . 5 4 , π‘š ∠ 𝐡 𝐢 𝐴 = 5 3 . 0 0 ∘
  • B 𝐴 𝐡 = 7 . 0 3 , 𝐴 𝐢 = 5 . 5 4 , π‘š ∠ 𝐡 𝐢 𝐴 = 5 2 . 0 0 ∘
  • C 𝐴 𝐡 = 7 . 0 9 , 𝐴 𝐢 = 5 . 5 4 , π‘š ∠ 𝐡 𝐢 𝐴 = 5 3 . 0 0 ∘
  • D 𝐴 𝐡 = 7 . 0 9 , 𝐴 𝐢 = 5 . 5 4 , π‘š ∠ 𝐡 𝐢 𝐴 = 5 2 . 0 0 ∘
  • E 𝐴 𝐡 = 6 . 5 8 , 𝐴 𝐢 = 6 . 1 4 , π‘š ∠ 𝐡 𝐢 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 , ,