# Worksheet: Law of Cosines

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

**Q2: **

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.

**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 cm^{2}. Find the other lengths and angles giving lengths to one
decimal place and angles to the nearest degree.

- A, , ,
- B, , ,
- C, , ,
- D, , ,

**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

**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.