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IGCSE Math B9 TrigonometryTopic Practice

9 Trigonometry

Edexcel IGCSE Math B 9 Trigonometry question practice helps you revise this syllabus point with the course map in view. Use this page to focus on one topic, check the style of questions available, and connect each attempt back to the knowledge area it is testing.

EduNinja keeps Math B practice aligned to Edexcel, so you can move from topic review into exam-style question bank work without losing the syllabus structure. Start with a small set, mark the weak steps, then return to nearby topic links when a definition, graph, calculation, or explanation needs repair.

Question 1

[Maximum number: 1]

The scale drawing opposite shows the positions, A, B and C, of three lighthouses. The points A, B and C lie at sea level in the same horizontal plane with B due north of A.

The scale of the drawing is 1 cm represents 50 km.

Question 1(a)

(a)

Find by measurement

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Question 1(a)(ii)

(i)

the bearing of C from A.

Question 1(c)

(b)
Question image

Given that S is east of the line AB,

find, by measurement, the bearing of S from A.

[ 1 ]

Question 1(b)

[Maximum number: 3]
Question image

Diagram NOT accurately drawn

In Figure 1, A, B, C and D are vertices of the regular 10-sided polygon ABCDEFGHIJ.
AB=BC=CD=6 cm and BC is parallel to AD.

Calculate the length, in cm to 3 significant figures, of AD.

Question 1

[Maximum number: 5]
Question image

Figure 1 shows a quadrilateral ABCD.
AB=9.3 cm,AC=5 cm,AD=10.8 cm.AB=9.3\text{ cm},\quad AC=5\text{ cm},\quad AD=10.8\text{ cm}.∠ACD=124∘,∠ACB=90∘,∠CAB=x∘,∠ADC=y∘.\angle ACD=124^\circ, \quad \angle ACB=90^\circ, \quad \angle CAB=x^\circ, \quad \angle ADC=y^\circ.
Calculate to one decimal place,

Question 1(a)

(a)

the value of x,

[ 2 ]

Question 1(b)

(b)

the value of y.

Sine rule:
asin⁡A=bsin⁡B=csin⁡C.\frac{a}{\sin A}=\frac{b}{\sin B}=\frac{c}{\sin C}.

[ 3 ]

Question 2

The bearing of village A from village B is 124∘124^\circ.
Find the bearing of village B from village A.

Question 2

Question image

The diagram shows the position of two towns, J and K.
The bearing of J from K is 214∘214^\circ.
Find the bearing, in degrees, of K from J.

Question 3

Question image

Diagram NOT accurately drawn

The diagram shows the position of two ports, A and B, and the position of a ship C
The bearing of port B from port A is 133∘133^{\circ}
Given that C is due west of B
calculate the value of x

x=

Question 14

[Maximum number: 4]
Question image

The diagram shows a triangle ABC.
The point D lies on AC so that BD is perpendicular to AC.

∠BAD=64∘,∠ACB=28∘,AD=2 cm.\angle BAD=64^\circ, \qquad \angle ACB=28^\circ, \qquad AD=2\text{ cm}.

Calculate the length, in cm to one decimal place, of BC.

Question 4

The bearing of Port A from Port B is 276∘276^\circ.
Find the bearing of Port B from Port A.

Question 2

[Maximum number: 4]
Question image

Diagram NOT accurately drawn.

Figure 1 shows part of a regular 16-sided polygon in which PA and AB are two sides.
Figure 1 also shows the isosceles triangle ABC in which AB=CB=5 cm.
PAC is a straight line.

Calculate the length, in cm to 3 significant figures, of AC.

Question 3

[Maximum number: 8]
Figure 2

Figure 2

Diagram NOT accurately drawn

Figure 2 shows a vertical tower AT of height 110 m and a horizontal triangle PAQ. The base A of the tower is 600 m due north of a point P.

Question 3(a)

(a)

Calculate the size, in degrees to one decimal place, of the angle of elevation of T from P.

[ 2 ]

Question 3(b)

(b)

The point Q is 900 m on a bearing of 065° from P.

Calculate the distance, in metres to 3 significant figures, of A from Q.

[ 3 ]

Question 3(c)

(c)

Calculate the bearing, in degrees to the nearest degree, of A from Q.

Sine rule: asin⁡A=bsin⁡B=csin⁡CCosine rule: a2=b2+c2−2bccos⁡A\begin{array}{c} \text{Sine rule: }\frac{a}{\sin A}=\frac{b}{\sin B}=\frac{c}{\sin C}\\[2mm] \text{Cosine rule: }a^2=b^2+c^2-2bc\cos A \end{array}

[ 3 ]
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