# Worksheet: Right Triangle Trigonometry: Solve for an Angle

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

**Q8: **

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

**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 measure 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 measures of and , in degrees, to two decimal places.

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

**Q15: **

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

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

**Q20: **

Given the following figure, find the measures of angles and and the length of . Give your answers to two decimal places.

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

**Q21: **

Find the measure of giving the answer to the nearest second.

- A
- B
- C
- D

**Q22: **

A palm tree 10.6 metres tall is observed from a point 12 metres away on the same horizontal plane as the base of the tree. Find the angle of elevation to the top of the palm tree giving the answer to the nearest minute.

- A
- B
- C
- D

**Q23: **

Find the value of giving the answer to the nearest second.

- A
- B
- C
- D

**Q24: **

Find the measure of given is a rectangle where and . Give the answer to the nearest second.

- A
- B
- C
- D

**Q25: **

Find the measure of giving the answer to the nearest second.

- A
- B
- C
- D