# 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.

**Q2: **

A house is 66 metres tall. The angle of elevation from the base of the house to the top of a tower is , and the angle of elevation from the top of the house to the top of the tower is . Find the height of the tower giving the answer to the nearest metre.

**Q3: **

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

**Q4: **

An aeroplane needs to head due north, but there is a wind blowing from the southwest at 60 km/h. The plane flies with an airspeed of 550 km/h. To end up flying due north, how many degrees west of north will the pilot need to fly the plane?

- A
- B
- C
- D
- E

**Q5: **

Ramy, Shady, and Engy stand at three points, , , and respectively. Suppose that , , and Ramy is exactly 12 feet away from Shady.

Find the distance between Shady and Engy, to two decimal places.

- A 9.38 feet
- B 14.51 feet
- C 9.12 feet
- D 9.93 feet
- E 5.61 feet

Find the distance between Ramy and Engy, to two decimal places.

- A 9.12 feet
- B 7.27 feet
- C 3.73 feet
- D 15.79 feet
- E 5.48 feet

**Q10: **

To determine how far a boat is from shore, two radar stations 500 feet apart find the angles out to the boat, as shown in the given figure. Determine the distance of the boat from station and the distance of the boat from shore. Round your answers to the nearest whole foot.

- A 442 ft, 531 ft
- B 565 ft, 193 ft
- C 442 ft, 193 ft
- D 565 ft, 531 ft
- E 613 ft, 576 ft

**Q11: **

The diagram shows an 8-foot solar panel mounted on the roof of a house. The roof is inclined at to the horizontal, and, for maximum yield, the solar panel is placed at to the horizontal. The solar panel is held in position by a vertical support. How long should the support be to hold the solar panel at an inclination of ? Give your answer to one decimal place.

**Q19: **

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?

- Acosine rule
- Bdouble angle rule
- Ctangent rule
- Dsine rule
- Eangles sum rule

**Q24: **

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

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