The smart way to improve grades

Comprehensive & curriculum aligned

Affordable pricing from £10/month

Finding Angles Using the Cosine Rule

In this worksheet, students find an angle given three sides of a triangle by using the cosine rule.

'Finding Angles Using the Cosine Rule' worksheet

Key stage:  KS 4

Curriculum topic:  Geometry and Measures

Curriculum subtopic:  Know the Exact Values of Sin, Cos and Tan

Difficulty level:  

down

Worksheet Overview

QUESTION 1 of 10

This worksheet is about finding angles using the cosine rule.

Look at  triangle ABC below

 

 The cosine rule states that:

a2 = b2 + c2 - 2bc cosA

We can use the cosine rule to find an angle when we know all three sides of a triangle.

The side of length a will be opposite the angle we are trying to find.

 

Example:

In  triangle PQR, which is not drawn to scale,

PQ = 9 cm, QR = 10 cm, and PR = 15 cm.

Use the cosine rule to find ∠PQR to the nearest degree.

 

Answer:

Using the cosine rule,

152 = 92 + 102 - 2 x 9 x 10 x cosθº

225 = 81 + 100 - 180cosθº

180cosθº = 81 + 100 - 225 = -44

cosθº = -44 ÷ 180 = -0.24444444....

θº = cos-1(-0.24444444...) = 104°

In  triangle PQR, which is not drawn to scale,

 

PQ = 9 cm, QR = 10 cm, and PR = 15 cm.

 

Use the cosine rule to find ∠QPR to the nearest degree.

 

(Just write the number)

 

In  triangle PQR, which is not drawn to scale,

 

PQ = 9 cm, QR = 10 cm, and PR = 15 cm.

 

Use the cosine rule to find ∠QRP to the nearest degree.

 

(Just write the number)

 

In  triangle PQR, which is not drawn to scale,

 

PQ = 4.5 cm, QR = 10 cm, and PR = 12 cm.

 

Calculate ∠PQR to the nearest degree.

 

(Just write the number)

 

In  triangle PQR, which is not drawn to scale,

 

PQ = 4.5 cm, QR = 10 cm, and PR = 12 cm.

 

Use the cosine rule to find ∠PRQ to the nearest degree.

 

(Just write the number)

 

In  triangle PQR, which is not drawn to scale,

 

PQ = 4.5 cm, QR = 10 cm, and PR = 12 cm.

 

Use the cosine rule to find ∠PRQ to the nearest degree.

 

(Just write the number)

 

In  triangle ABC, which is not drawn to scale,

 

AB = 10 cm, BC = 6 cm, and AC = 12 cm.

 

Use the cosine rule to find ∠ABC to the nearest degree.

 

(Just write the number)

In  triangle ABC, which is not drawn to scale,

 

AB = 10 cm, BC = 6 cm, and AC = 12 cm.

 

Use the cosine rule to find ∠BAC to the nearest degree.

 

(Just write the number)

In  triangle ABC, which is not drawn to scale,

 

AB = 10 cm, BC = 6 cm, and AC = 8 cm.

 

Use the cosine rule to find ∠ACB to the nearest degree.

 

(Just write the number)

In  triangle ABC, which is not drawn to scale,

 

AB = 10 cm, BC = 10 cm, and AC = 10 cm.

 

Use the cosine rule to find ∠ACB to the nearest degree.

 

(Just write the number)

In  triangle ABC, which is not drawn to scale,

 

a = 10 cm, b = 5.5 cm, and c = 12 cm.

 

Use the cosine rule to find ∠A to the nearest degree.

 

(Just write the number)

  • Question 1

In  triangle PQR, which is not drawn to scale,

 

PQ = 9 cm, QR = 10 cm, and PR = 15 cm.

 

Use the cosine rule to find ∠QPR to the nearest degree.

 

(Just write the number)

 

CORRECT ANSWER
40
EDDIE SAYS
10² = 9² + 15² - 2 × 9 × 15 × cosθ°
  • Question 2

In  triangle PQR, which is not drawn to scale,

 

PQ = 9 cm, QR = 10 cm, and PR = 15 cm.

 

Use the cosine rule to find ∠QRP to the nearest degree.

 

(Just write the number)

 

CORRECT ANSWER
36
EDDIE SAYS
9² = 10² + 15² - 2 × 10 × 15 × cosθ°
  • Question 3

In  triangle PQR, which is not drawn to scale,

 

PQ = 4.5 cm, QR = 10 cm, and PR = 12 cm.

 

Calculate ∠PQR to the nearest degree.

 

(Just write the number)

 

CORRECT ANSWER
22
EDDIE SAYS
12² = 10² + 4.5² - 2 × 10 × 4.5 × cosθ°
  • Question 4

In  triangle PQR, which is not drawn to scale,

 

PQ = 4.5 cm, QR = 10 cm, and PR = 12 cm.

 

Use the cosine rule to find ∠PRQ to the nearest degree.

 

(Just write the number)

 

CORRECT ANSWER
21
EDDIE SAYS
4.5² = 10² + 12² - 2 × 10 × 12 × cosθ°
  • Question 5

In  triangle PQR, which is not drawn to scale,

 

PQ = 4.5 cm, QR = 10 cm, and PR = 12 cm.

 

Use the cosine rule to find ∠PRQ to the nearest degree.

 

(Just write the number)

 

CORRECT ANSWER
53
EDDIE SAYS
10² = 4.5² + 12² - 2 × 4.5 × 12 × cosθ°
  • Question 6

In  triangle ABC, which is not drawn to scale,

 

AB = 10 cm, BC = 6 cm, and AC = 12 cm.

 

Use the cosine rule to find ∠ABC to the nearest degree.

 

(Just write the number)

CORRECT ANSWER
94
EDDIE SAYS
12² = 10² + 6² - 2 × 10 × 6 × cosθ°
  • Question 7

In  triangle ABC, which is not drawn to scale,

 

AB = 10 cm, BC = 6 cm, and AC = 12 cm.

 

Use the cosine rule to find ∠BAC to the nearest degree.

 

(Just write the number)

CORRECT ANSWER
30
EDDIE SAYS
6² = 10² + 12² - 2 × 10 × 12 × cosθ°
  • Question 8

In  triangle ABC, which is not drawn to scale,

 

AB = 10 cm, BC = 6 cm, and AC = 8 cm.

 

Use the cosine rule to find ∠ACB to the nearest degree.

 

(Just write the number)

CORRECT ANSWER
90
EDDIE SAYS
10² = 6² + 8² - 2 × 6 × 8 × cosθ°
This is a 6, 8, 10 Pythagorean Triad.
  • Question 9

In  triangle ABC, which is not drawn to scale,

 

AB = 10 cm, BC = 10 cm, and AC = 10 cm.

 

Use the cosine rule to find ∠ACB to the nearest degree.

 

(Just write the number)

CORRECT ANSWER
60
EDDIE SAYS
10² = 10² + 10² - 2 × 10 × 10 × cosθ°
This is an equilateral triangle.
  • Question 10

In  triangle ABC, which is not drawn to scale,

 

a = 10 cm, b = 5.5 cm, and c = 12 cm.

 

Use the cosine rule to find ∠A to the nearest degree.

 

(Just write the number)

CORRECT ANSWER
56
EDDIE SAYS
10² = 5.5² + 12² - 2 × 5.5 × 12 × cosθ°
---- OR ----

Sign up for a £1 trial so you can track and measure your child's progress on this activity.

What is EdPlace?

We're your National Curriculum aligned online education content provider helping each child succeed in English, maths and science from year 1 to GCSE. With an EdPlace account you’ll be able to track and measure progress, helping each child achieve their best. We build confidence and attainment by personalising each child’s learning at a level that suits them.

Start your £1 trial

Start your trial for £1