# Worksheet: Law of Cosines

Q1:

In the given figure, using the law of cosines, find . Give your answer to two decimal places.

Q2:

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

Q3:

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

Q4:

In the given figure, using the law of cosines, find . Give your answer to two decimal places.

Q5:

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

Q6:

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

Q7:

, , and are three cities. Find the distance between cities and , giving your answer to the nearest kilometer.

• A12 km
• B16 km
• C21 km
• D23 km

Q8:

A plane travels 800 meters along the runway before taking off at an angle of . It travels a further meters at this angle as seen in the figure. Work out the distance of the plane from its starting point. Give your answer to 2 decimal places.

• A253.59 meters
• B meters
• C meters
• D meters
• E meters

Q9:

The shown diagram represents a satellite calculating the distances and the angle. Find the distance between the two cities. Give your answer to one decimal place. Note that the diagram is not to scale.

Q10:

A surveyor takes measurements as shown in the diagram. Calculate the distance across the lake. Give your answer to one decimal place.