# Worksheet: Law of Cosines

Q1:

is a triangle, where , , and . Find the value of , giving your answer to three decimal places.

Q2:

is a triangle, where , , and . Find the value of , giving your answer to three decimal places.

Q3:

Find all the angles in the triangle giving the answers to the nearest second.

• A , ,
• B , ,
• C , ,
• D , ,

Q4:

is a triangle where , , and . Find the measure of the largest angle in , giving the answer to the nearest second.

• A
• B
• C
• D

Q5:

is a triangle where , , and . Find the measure of the largest angle in , giving the answer to the nearest second.

• A
• B
• C
• D

Q6:

is a triangle where and . Find giving the answer to the nearest second.

• A
• B
• C
• D

Q7:

is a triangle where cm, cm and cm. Find the smallest angle in giving the answer to the nearest second.

• A
• B
• C
• D
• E

Q8:

The lengths of two sides of a triangle are and and the angle between them is . Find the length of the third side giving the answer in an exact form.

• A 53 cm
• B cm
• C cm
• D cm

Q9:

A biker travelled from city to city via city with a uniform speed of 52 km/h. He then returned directly to city with a uniform speed of 89 km/h. Find, in minutes, the total time of his whole journey to two decimal places.

Q10:

Find all the other angles and lengths of the triangle giving lengths to two decimal places and angles to the nearest second.

• A , ,
• B , ,
• C , ,
• D , ,