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Finding the Length of a Side Using the Sine Rule

In this worksheet, students find the length of a side given two angles and an opposite side in a triangle by using the sine rule.

'Finding the Length of a Side Using the Sine 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 the length of a side using the sine rule.

Look at  triangle ABC below

 

 The sine rule states that:

 

a = b = c
sin A sin B sin C

 

We can use the sine rule to find the length of a side when we know two angles and an opposite side.

 

Example:

In  triangle PQR, which is not drawn to scale,

PQ = 7 cm, ∠QPR = 72° and ∠PRQ = 24°.

Use the sine rule to find the length of PR in cm to 1 dp.

 

Answer:

First we must find ∠PQR = 180° - 72° - 24° = 84°.

 

Using the sine rule,

 

PR = 7
sin 84° sin 24°

 

PR = 7 x sin 84°
sin 24°

 

PR = 7 x sin 84° ÷ sin 24°

PR = 17.1 cm

In  triangle PQR, which is not drawn to scale,

 

PQ = 7 cm, ∠QPR = 72° and ∠PRQ = 24°

 

Use the sine rule to find the length of QR in cm to 1 dp.

 

(Just write the number)

 

In  triangle PQR, which is not drawn to scale,

 

QR = 18 cm, ∠QPR = 72° and ∠PQR = 100°

 

Use the sine rule to find the length of PR in cm to 1 dp.

 

(Just write the number)

 

In  triangle PQR, which is not drawn to scale,

 

PQ = 9 cm, ∠QPR = 32° and ∠PRQ = 38°

 

Use the sine rule to find the length of QR in cm to 1 dp.

 

(Just write the number)

 

In  triangle PQR, which is not drawn to scale,

 

PR = 19 cm, ∠PQR = 102° and ∠PRQ = 37°

 

Use the sine rule to find the length of PQ in cm to 1 dp.

 

(Just write the number)

 

In  triangle PQR, which is not drawn to scale,

 

QR = 18 cm, ∠QPR = 72° and ∠PQR = 100°

 

Use the sine rule to find the length of PQ in cm to 1 dp.

 

(Just write the number)

 

In  triangle PQR, which is not drawn to scale,

 

PQ = 9 cm, ∠QPR = 32° and ∠PRQ = 38°

 

Use the sine rule to find the length of PR in cm to 1 dp.

 

(Just write the number)

 

In  triangle PQR, which is not drawn to scale,

 

PR = 19 cm, ∠PQR = 102° and ∠PRQ = 37°

 

Use the sine rule to find the length of QR in cm to 1 dp.

 

(Just write the number)

 

In  triangle PQR, which is not drawn to scale,

 

PR = 12 cm, ∠PQR = 95° and ∠QPR = 62°

 

Use the sine rule to find the length of QR in cm to 1 dp.

 

(Just write the number)

 

In  triangle PQR, which is not drawn to scale,

 

PR = 12 cm, ∠PQR = 95° and ∠QPR = 62°

 

Use the sine rule to find the length of PQ in cm to 1 dp.

 

(Just write the number)

 

In  triangle ABC, which is not drawn to scale,

 

b = 6.5 cm, ∠CBA = 65° and ∠BCA = 65°

 

Use the sine rule to find the length of AB in cm to 1 dp.

 

(Just write the number)

 

  • Question 1

In  triangle PQR, which is not drawn to scale,

 

PQ = 7 cm, ∠QPR = 72° and ∠PRQ = 24°

 

Use the sine rule to find the length of QR in cm to 1 dp.

 

(Just write the number)

 

CORRECT ANSWER
16.4
EDDIE SAYS
QR = 7
sin 72° sin 24°
  • Question 2

In  triangle PQR, which is not drawn to scale,

 

QR = 18 cm, ∠QPR = 72° and ∠PQR = 100°

 

Use the sine rule to find the length of PR in cm to 1 dp.

 

(Just write the number)

 

CORRECT ANSWER
18.6
EDDIE SAYS
PR = 18
sin 100° sin 72°
  • Question 3

In  triangle PQR, which is not drawn to scale,

 

PQ = 9 cm, ∠QPR = 32° and ∠PRQ = 38°

 

Use the sine rule to find the length of QR in cm to 1 dp.

 

(Just write the number)

 

CORRECT ANSWER
7.7
EDDIE SAYS
QR = 9
sin 32° sin 38°
  • Question 4

In  triangle PQR, which is not drawn to scale,

 

PR = 19 cm, ∠PQR = 102° and ∠PRQ = 37°

 

Use the sine rule to find the length of PQ in cm to 1 dp.

 

(Just write the number)

 

CORRECT ANSWER
11.7
EDDIE SAYS
PQ = 19
sin 37° sin 102°
  • Question 5

In  triangle PQR, which is not drawn to scale,

 

QR = 18 cm, ∠QPR = 72° and ∠PQR = 100°

 

Use the sine rule to find the length of PQ in cm to 1 dp.

 

(Just write the number)

 

CORRECT ANSWER
2.6
EDDIE SAYS
Missing angle = 180° - 100° - 72° = 8°
PQ = 18
sin 8° sin 72°
  • Question 6

In  triangle PQR, which is not drawn to scale,

 

PQ = 9 cm, ∠QPR = 32° and ∠PRQ = 38°

 

Use the sine rule to find the length of PR in cm to 1 dp.

 

(Just write the number)

 

CORRECT ANSWER
13.7
EDDIE SAYS
Missing angle = 180° - 32° - 38° = 110°
PR = 9
sin 110° sin 38°
  • Question 7

In  triangle PQR, which is not drawn to scale,

 

PR = 19 cm, ∠PQR = 102° and ∠PRQ = 37°

 

Use the sine rule to find the length of QR in cm to 1 dp.

 

(Just write the number)

 

CORRECT ANSWER
12.7
EDDIE SAYS
Missing angle = 180° - 102° - 37° = 41°
QR = 19
sin 41° sin 102°
  • Question 8

In  triangle PQR, which is not drawn to scale,

 

PR = 12 cm, ∠PQR = 95° and ∠QPR = 62°

 

Use the sine rule to find the length of QR in cm to 1 dp.

 

(Just write the number)

 

CORRECT ANSWER
10.6
EDDIE SAYS
QR = 12
sin 62° sin 95°
  • Question 9

In  triangle PQR, which is not drawn to scale,

 

PR = 12 cm, ∠PQR = 95° and ∠QPR = 62°

 

Use the sine rule to find the length of PQ in cm to 1 dp.

 

(Just write the number)

 

CORRECT ANSWER
4.7
EDDIE SAYS
Missing angle = 180° - 95° - 62° = 23°
PQ = 12
sin 23° sin 95°
  • Question 10

In  triangle ABC, which is not drawn to scale,

 

b = 6.5 cm, ∠CBA = 65° and ∠BCA = 65°

 

Use the sine rule to find the length of AB in cm to 1 dp.

 

(Just write the number)

 

CORRECT ANSWER
6.5
EDDIE SAYS
c = 6.5
sin 65° sin 65°

The triangle is isosceles
---- OR ----

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