# Worksheet: Applications of Inverse Trigonometric Functions in a Right Triangle

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

**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

**Q10: **

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

- A , ,
- B , ,
- C , ,
- D , ,
- E , ,

**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: **

is a right-angled triangle at where and . Find the lengths of and and the measure of .

- A , ,
- B , ,
- C , ,
- D , ,

**Q13: **

For the given figure, find angle , 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: **

is a right-angled triangle at where and . Find the length , giving the answer to the nearest centimetre, and the measure of angles and , giving the answer to the nearest degree.

- A , ,
- B , ,
- C , ,
- D , ,

**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 . Determine the height, , at which the top of the ladder touches the wall, the angle between the top of the ladder and the wall, , and the distance, , between the bottom of the ladder and the base of the wall. If necessary, round your answers to two decimal places.

- A m, , m
- B m, , m
- C m, , m
- D m, , m
- E m, , m

**Q19: **

is a right-angled triangle at where and . Find the length , giving the answer to the nearest centimetre, and the measure of angles and , giving the answer to the nearest degree.

- A , ,
- B , ,
- C , ,
- D , ,