# Worksheet: Right Triangle Trigonometry: Solve for a Side

In this worksheet, we will practice finding the value of a missing side length in a right triangle by choosing the appropriate trigonometric ratio for a given angle.

**Q7: **

Find the length of , given that , , and .

- A cm
- B cm
- C cm
- D cm
- E cm

**Q9: **

is an isosceles triangle where , and . Find the length of giving the answer to one decimal place.

**Q10: **

Find the length of given is a right-angled triangle at where and .

**Q11: **

A kite has a string of length 75 meters. The angle the string makes with the horizontal ground is . Find the height of the kite from the ground giving the answer to two decimal places.

**Q12: **

is a triangle where , , and . Point lies on where . Find the height of the triangle drawn from point to giving the answer to two decimal places.

**Q13: **

is a rectangle where and . Find the lengths of and giving the answer to three decimal places.

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

**Q15: **

In the given figure, , , and . Unless otherwise stated, give all solutions to the following questions to four decimal places.

Work out the length of and .

- A2.8512, 7.1488
- B3.2184, 6.7816
- C1.7101, 8.2899
- D3.2899, 6.7101
- E4.6985, 5.3015

Using the Pythagorean theorem, or otherwise, calculate .

Work out . Give your answer to two decimal places.

**Q16: **

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

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

**Q17: **

In the given figure, given that and , find the lengths of and and the measure of in degrees. Give your answers to two decimal places.

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

**Q18: **

Find in the given figure. Give your answer to two decimal places.

**Q19: **

Find given is a triangle where and .

**Q20: **

Find given is a right-angled triangle at where .

**Q21: **

Find the values of and giving the answer to three decimal places.

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

**Q22: **

Find the values of and giving the answer to three decimal places.

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

**Q23: **

is a right-angled triangle at , where , , and . Find the measure of giving the answer to the nearest second.

- A
- B
- C
- D

**Q24: **

Find the value of , given that is a triangle, where , , and is drawn perpendicular to intersecting at .

- A
- B
- C
- D

**Q25: **

Find the value of given is a right-angled triangle at where .

- A168
- B600
- C175
- D625