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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.

Q1:

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

Q4:

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

Q5:

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

Q6:

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

Q7:

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

Q8:

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

Q9:

Q10:

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

Q11:

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

Q12:

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

Q13:

Given the following figure, find the lengths of π΄ π΅ and π΅ πΆ and the measure of β π΄ πΆ π΅ in degrees. Give your answers to two decimal places.

Q14:

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

Q15:

π΄ π΅ πΆ is a right-angled triangle at π΅ where π΅ πΆ = 2 5 c m and π β π΄ = 5 8 β . Find the lengths of π΄ πΆ and π΄ π΅ .

Q16:

Q17:

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

Q18:

Q19:

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