# Worksheet: Right Triangle Trigonometry

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

**Q8: **

A person observes a point on the ground from the top of a hill that is 1.56 km high. The angle of depression is . Find the distance between the point and the observer giving the answer to the nearest metre.

**Q9: **

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

**Q10: **

In the given figure, find . Give your answer to two decimal places.

**Q11: **

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

**Q13: **

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.

**Q14: **

The angle of elevation between an aeroplane 10,000 m high and a person on a point on the ground is . Find the distance between the point and the aeroplane giving the answer to the nearest metre.

**Q15: **

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.

**Q16: **

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

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

**Q18: **

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 .

- A3.2184, 6.7816
- B4.6985, 5.3015
- C1.7101, 8.2899
- D2.8512, 7.1488
- E3.2899, 6.7101

Using the Pythagorean theorem, or otherwise, calculate .

Work out . Give your answer to two decimal places.

**Q19: **

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

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

**Q20: **

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 , ,