In this worksheet, we will practice using the cosine law to solve real-world problems.

**Q2: **

An aeroplane flies 220 miles on a bearing of and then changes course and flies 180 miles on a bearing of . How far is the plane from its starting point and on what bearing? Give your answers to one decimal place.

- A 52.9 miles,
- B 172.9 miles,
- C miles,
- D 172.9 miles,
- E 362.9 miles,

**Q3: **

A 113-foot tower is located on a hill that is inclined to the horizontal, as shown in the figure. A guy wire is to be attached to the top of the tower and anchored at a point 98 feet uphill from the base of the tower. Find the length of wire needed.

**Q4: **

Two planes leave the same airport at the same time. One flies on a bearing of at 500 miles per hour. The other flies on a bearing of at 600 miles per hour. How far apart are the planes after 2 hours?

**Q5: **

Two ships left a port at the same time. One traveled on a bearing of at 18 mph, while the other traveled on a bearing of at 22 mph. Find the distance between the ships after 10 hours. Give your answer to the nearest mile.

**Q6: **

A plane follows a straight path at a steady speed of 600 miles per hour. After 1 hour 30 minutes, the pilot makes a course correction of , and the flight continues at the same speed, following a straight path, for another 2 hours. How far is the plane from its initial position? Give your answer to the nearest mile.

**Q7: **

A man ran 24 km down a straight road. He then turned and ran a further 9 km along another straight road. Find, to the nearest kilometre, the shortest distance between his start and end points.

**Q8: **

Two boats leave a harbor in different directions. One travels due west at 30 mph, and the other travels on a bearing of at 42 mph. How far apart are they after 90 minutes?