# Worksheet: Law of Cosines

In this worksheet, we will practice finding the sides and angles in non-right triangles using the law of cosines.

Q1:

and are two hot air balloons flying at heights 117 m and 84 m respectively. The angles of depression at a point on the ground from and are and respectively. Find the distance between the balloons giving the answer to the nearest meter. 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:

, , and are three cities. Find the distance between cities and , giving your answer to the nearest kilometer. Q7:

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

Q8:

A biker traveled 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. Q9:

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

Q10:

is a triangle where , and the area is cm2. Find the other lengths and angles giving lengths to one decimal place and angles to the nearest degree.

• A, , ,
• B, , ,
• C, , ,
• D, , ,

Q11:

The side lengths of a triangle are , , and . Emma calculated, to one decimal place, the measures of the corresponding angles as , , and . Was she correct?

• Ayes
• Bno

Q12:

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

Q13:

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

• A
• B
• C
• D

Q14:

is a triangle where , and the perimeter is 148 cm. Find the largest angle in giving the answer to the nearest second.

• A
• B
• C
• D

Q15:

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

• A
• B
• C
• D

Q16:

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

• A
• B
• C
• D

Q17:

Find the value of to 2 decimal places given that the measure of Angle is , is 10 cm, and is 16 cm. Q18:

For the triangle given, find the value of the three angles to the nearest degree. • A, ,
• B, ,
• C, ,
• D, ,
• E, ,

Q19:

Find to one decimal place. Q20:

Complete the expression for triangle : .

• A
• B
• C
• D

Q21:

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

• A
• B
• C
• D

Q22:

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

• A
• B
• C
• D

Q23:

Which rule could be used to find the length of an unknown side of a triangle, given the other two lengths and the measure of their included angle.

• Asine rule
• Bdouble angle rule
• Ccosine rule
• Dtangent rule
• Eangles sum rule

Q24:

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

• A
• B
• C
• D

Q25:

Circle has a radius of 8 cm where the length is 5 cm. Find the angle in radians giving the answer to two decimal places. 