# 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.

**Q12: **

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
- Dangles sum rule
- Etangent rule

**Q16: **

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

- AThe actual distance between cities and is 12 km, and the actual distance between cities and is 21 km.
- BThe actual distance between cities and is 36 km, and the actual distance between cities and is 21 km.
- CThe actual distance between cities and is 12 km, and the actual distance between cities and is 7 km.
- DThe actual distance between cities and is 9 km, and the actual distance between cities and is 16 km.

**Q20: **

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

**Q21: **

In the given figure, is a rectangle and is a point on the straight line . , , and . Find the length of giving the answer to the nearest meter.

**Q22: **

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

**Q23: **

, 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 .

**Q24: **

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

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

**Q25: **

is a triangle, where cm, cm, and . Find all possible values of length giving the answer to three decimal places.

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