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Cosine Rule Problems and Solutions

This document contains 11 math problems involving trigonometry and calculating unknown side lengths or angles of triangles using trigonometric functions like sine, cosine and tangent. The problems provide diagrams of triangles with some side lengths or angles given and ask the reader to calculate the missing information. The reader is instructed to show their work and round their answers to a specified number of decimal places or significant figures.

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Maged Yassa
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We take content rights seriously. If you suspect this is your content, claim it here.
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256 views8 pages

Cosine Rule Problems and Solutions

This document contains 11 math problems involving trigonometry and calculating unknown side lengths or angles of triangles using trigonometric functions like sine, cosine and tangent. The problems provide diagrams of triangles with some side lengths or angles given and ask the reader to calculate the missing information. The reader is instructed to show their work and round their answers to a specified number of decimal places or significant figures.

Uploaded by

Maged Yassa
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
Available Formats
Download as PDF, TXT or read online on Scribd
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Name: ___________________________

The Cosine

Rule
1
100º

13 cm 10 cm

x cm
Work out the value of x.
Give your answer to 1 decimal place.

…..........................
(Total for question 1 is 3 marks)

B
2

5m

42º
A

7m C

Work out the length of BC.


Give your answer to 3 significant figures.

…..........................m
(Total for question 2 is 3 marks)
A
3

15 cm

B 20º
12 cm C

Work out the length of AB.


Give your answer to 1 decimal place.

…..........................cm
(Total for question 3 is 3 marks)

A
4

xm 5.3 m

B 43º
6.2 m C

Work out the value of x.


Give your answer to 3 significant figures.

…..........................
(Total for question 4 is 3 marks)
5 xº

15 cm 16 cm

20 cm
Work out the value of x.
Give your answer to 3 significant figures.

…..........................
(Total for question 5 is 3 marks)

A
6

10 m
5m

B C
9m
Work out the size of angle ABC
Give your answer to the nearest degree.

…..........................o
(Total for question 6 is 3 marks)
7
xº

21 cm 13 cm

24 cm
Work out the value of x.
Give your answer to 1 decimal place.

…..........................
(Total for question 7 is 3 marks)

B
8

5.2 m

6.9 m

7.3 m C

Work out the size of angle BAC.


Give your answer to 3 significant figures.

…..........................o
(Total for question 8 is 3 marks)
9
10 cm

40º

xº
13 cm
5 cm
Work out the value of x.
Give your answer to 1 decimal place.

…..........................
(Total for question 9 is 5 marks)
10

(x + 2) 73

60º

(2x – 3)

Work out the value of x.

…..........................
(Total for question 10 is 5 marks)
A
11

15.4 m
19.7 m

B C

The area of the triangle is 100m2


Calculate the perimeter of triangle ABC.
Give your answer to 3 significant figures.

…..........................m
(Total for question 11 is 5 marks)

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