# Worksheet: Law of Sines

In this worksheet, we will practice applying the law of sines to find lengths and angle measures in non-right triangles.

**Q1: **

is a triangle where , and . Find the length of giving the answer to two decimal places.

**Q13: **

Which rule could be used to find the length of an unknown side of a triangle, given the measures of two angles and the length of one other side?

- Asine rule
- Bcosine rule
- Cdouble angle rule
- Dtangent rule
- Eangles sum rule

**Q17: **

The scale of a map is . The positions of three towns on a map form a triangle. Towns B and C are 17 cm apart, and the angles and are and respectively. Find the actual distance between towns A and B and between towns A and C, giving the answer to the nearest kilometer.

- A The actual distance between cities A and B is 12 km, and the actual distance between cities A and C is 7 km.
- B The actual distance between cities A and B is 12 km, and the actual distance between cities A and C is 21 km.
- C The actual distance between cities A and B is 36 km, and the actual distance between cities A and C is 21 km.
- D The actual distance between cities A and B is 9 km, and the actual distance between cities A and C is 16 km.

**Q21: **

is a triangle, where , , and length . Find the length of the shortest side of giving the answer to one decimal place.

**Q22: **

In the figure below, , and . Find the length of giving the answer to the nearest metre.

**Q23: **

is a triangle where and . Find length giving the answer to two decimal places.

**Q24: **

, and represent three coffee shops along a river bank. is on one side and and are on the other. is located where and . Find the distance between and and the width of the river giving the answers to two decimal places.

- A . Width of river .
- B . Width of river .
- C . Width of river .
- D . Width of river .

**Q25: **

is a triangle where , and . Find all possible values of giving the answer to the nearest second.

- A
- B or
- C
- D or
- E or