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Sine, cosine rules for SQA National 5 Maths

Sine, cosine rules

This page covers the following topics:

1. Sine rule
2. Problems with sine rule
3. Cosine rule
4. Problems with cosine rule

Sine rule

When solving word problems with the sine rule it is best to draw a picture and label the known angles/side lengths.

Problems with sine rule

Cosine rule

When solving word problems with the cosine rule it is best to draw a picture and label the known angles/side lengths.

Problems with cosine rule

1

Use the cosine rule to find angle A, given a = 5, b = 7 and c = 6.

44.4ยบ

Use the cosine rule to find angle A, given a = 5, b = 7 and c = 6.

2

Find the length of pole A. Give your answer with two decimal places.

12.45 m

Find the length of pole A. Give your answer with two decimal places.

3

The diagram shows a ladder propped against a slightly slanted wall. Find the angle between the ladder and the wall.

27.7ยบ

The diagram shows a ladder propped against a slightly slanted wall. Find the angle between the ladder and the wall.

4

A triangle is created using 3 poles. The poles are 20 m, 25 m and 23 m in length. Find the angle between the 20 m and 23 m poles.

70.7ยบ

A triangle is created using 3 poles. The poles are 20 m, 25 m and 23 m in length. Find the angle between the 20 m and 23 m poles.

5

Two match sticks are held up with their tips against each other. Both match sticks are 5 cm long. The angle between them is 65ยบ. Find the distance between the bottom of the match sticks along the ground.

5.37 cm

Two match sticks are held up with their tips against each other. Both match sticks are 5 cm long. The angle between them is 65ยบ. Find the distance between the bottom of the match sticks along the ground.

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