Sine, Cosine Rule & Area of Triangles Practice Questions

Question 1

3 marks

You may use a calculator for this question.

The diagram shows triangle $ABC$ .

Diagram NOT accurately drawn

Work out the length of $AC$ .

Give your answer correct to 3 significant figures.

....................................................... cm

/ 3

Question 2

2 marks

You may use a calculator for this question.

In triangle $PQR$ , $PQ = 7.2$ cm, $QR = 9.5$ cm and angle $PQR = 118^\circ$ .

Work out the area of triangle $PQR$ .

Give your answer correct to 1 decimal place.

....................................................... cm $^2$

/ 2

Question 0

7 marks

You may use a calculator for this question.

A boat sails from a harbour $P$ on a bearing of $040^\circ$ for $15$ km to a buoy $Q$ .

It then sails from $Q$ on a bearing of $125^\circ$ for $22$ km to a lighthouse $R$ .

You may find it helpful to draw a diagram.

(a)

Work out the distance $PR$ .

Give your answer correct to 3 significant figures.

....................................................... km

/ 4

(b)

Work out the bearing of $R$ from $P$ .

Give your answer correct to 1 decimal place.

....................................................... $^\circ$

/ 3

Question 0

5 marks

You may use a calculator for this question.

In triangle $ABC$ , $AB = 9.1$ cm, $BC = 12.4$ cm and $AC = 16.8$ cm.

(a)

Work out the size of angle $ABC$ .

Give your answer correct to 1 decimal place.

....................................................... $^\circ$

/ 3

(b)

Work out the area of triangle $ABC$ .

Give your answer correct to 3 significant figures.

....................................................... cm $^2$

/ 2

Question 0

5 marks

You may use a calculator for this question.

$ABC$ and $ACD$ are triangles.

Diagram NOT accurately drawn

Work out the length of $CD$ .

Give your answer correct to 3 significant figures.

....................................................... cm

/ 5

Question 0

6 marks

You may use a calculator for this question.

In triangle $PQR$ , $PQ = 13$ cm and angle $PQR = 63^\circ$ .

The area of triangle $PQR$ is $42$ cm $^2$ .

(a)

Work out the length of $QR$ .

Give your answer correct to 3 significant figures.

....................................................... cm

/ 3

(b)

Work out the length of $PR$ .

Give your answer correct to 3 significant figures.

....................................................... cm

/ 3

Question 0

3 marks

You may use a calculator for this question.

In triangle $ABC$ , $AB = 9$ cm and $BC = 14$ cm.

The area of triangle $ABC$ is $50$ cm $^2$ .

Angle $ABC$ is obtuse.

Work out the size of angle $ABC$ .

Give your answer correct to 1 decimal place.

....................................................... $^\circ$

/ 3

Question 0

5 marks

Do not use a calculator for this question.

$ABCD$ is a parallelogram.

$AB = 2x$ cm, $BC = 3x$ cm and angle $ABC = 120^\circ$ .

Diagram NOT accurately drawn

Prove that $AC^2 : BD^2 = 19 : 7$ .

/ 5

Question 0

5 marks

You may use a calculator for this question.

The diagram shows triangle $PQR$ .

$PQ = (2x-1)$ cm, $QR = (x+4)$ cm and angle $PQR = 150^\circ$ .

The area of triangle $PQR$ is $15$ cm $^2$ .

Diagram NOT accurately drawn

(a)

Show that $2x^2 + 7x - 64 = 0$ .

/ 3

(b)

Work out the length of $QR$ .

Give your answer correct to 3 significant figures.

....................................................... cm

/ 2

Question 0

7 marks

You may use a calculator for this question.

The diagram shows triangle $ABC$ .

$AB = 10$ cm, $BC = 13$ cm. $D$ is the point on $AC$ with $AD = 3$ cm and $DC = 4$ cm.

Diagram NOT accurately drawn

(a)

Work out the length of $BD$ .

Give your answer correct to 3 significant figures.

....................................................... cm

/ 4

(b)

Work out the area of triangle $BCD$ .

Give your answer correct to 3 significant figures.

....................................................... cm $^2$

/ 3

Number Operations & Integers

Fractions, Decimals & Percentages

Indices & Surds

Approximation & Estimation

Ratio, Proportion & Rates of Change

Algebra

Graphs of Equations & Functions

Basic Geometry

Congruence, Similarity, Vectors & Transformations

Mensuration, Lengths, Areas & Volumes

Probability

Statistics

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