The diagram represents a tent in the shape of a triangular prism. The front of the tent, A B D , is an isosceles triangle with A B = A D . The width B D is 1 . 8 m and the supporting pole A C is perpendicular to B D and 1 . 5 m high. The tent is 3 m long. Calculate the angle between A B and B D .

A B D is an isosceles triangle. So, the perpendicular A C bisects B D and ∠ D A B . B D = 2 B C ⇒ B C = 1 2 × B D ⇒ B C = 1 2 × 1 . 8 ⇒ B C = 0 . 9 m ∠ A B C can be found by using inverse tan function. tan ( ∠ A B C ) = A C B C ⇒ tan ( ∠ A B C ) = 1 . 5 0 . 9 ⇒ ∠ A B C = tan - 1 1 . 5 0 . 9 From the calculator, we get, ∠ A B C = 59 . 0 °

The diagram represents a tent in the shape of a triangular prism. The front of the tent, A B D , is an isosceles triangle with A B = A D . The width B D is 1 . 8 m and the supporting pole A C is perpendicular to B D and 1 . 5 m high. The tent is 3 m long. Calculate the length of A B .

A B D is an isosceles triangle. So, the perpendicular A C bisects B D and ∠ D A B . B D = 2 B C ⇒ B C = 1 2 × B D ⇒ B C = 1 2 × 1 . 8 ⇒ B C = 0 . 9 m AB can be found by using either sin or cos function Here, we will use cos function. cos ( ∠ A B C ) = B C A B ⇒ cos ( 59 . 0 ° ) = 0 . 9 A B ⇒ 0 . 515 = 0 . 9 A B ⇒ A B = 1 . 749 m

The diagram represents a tent in the shape of a triangular prism. The front of the tent, A B D , is an isosceles triangle with A B = A D . The width B D is 1 . 8 m and the supporting pole A C is perpendicular to B D and 1 . 5 m high. The tent is 3 m long. Calculate the capacity inside the tent (i.e. volume).

The volume is given by: Here base is a triangle. V = base area × height V = area A B D × 3 Area A B D = 1 2 × B D × A C ⇒ Area A B D = 1 2 × 1 . 8 × 1 . 5 ⇒ Area A B D = 1 . 35 m 2 So, V = 1 . 35 × 3 ⇒ V = 4 . 05 m 3 Hence, capacity of tent is 4 . 05 m 3 .

The sketch represents a field P Q R S on level ground. The sides P Q and S R run due east. Write down the bearing of S from P . Enable Ginger Cannot connect to Ginger Check your internet connection or reload the browser Disable in this text field Rephrase Rephrase current sentence Edit in Ginger ×

The bearing of S from P can be represented as: From the figure, ∠ N S R = ∠ S P Q (corresponding angles) ∠ M S R = 90 ° So, ∠ M S N = ∠ M S R - ∠ N S R ⇒ ∠ M S N = 90 ° - 70 ° ⇒ ∠ M S N = 20 ° So the bearing of S from P is 20 ° .

EASY

Upper Secondary: IGCSE

IMPORTANT

Earn 100

The diagram represents a ramp $A B$ for a lifeboat. $A C$ is vertical and $C B$ is horizontal.
Calculate the size of $∠ A B C$ correct to $1$ decimal place.

Important Questions on Scale Drawings, Bearings and Trigonometry

EASY

Upper Secondary: IGCSE

IMPORTANT

Cambridge IGCSE® Mathematics Core and Extended Coursebook Second Edition>Chapter 15 - Scale Drawings, Bearings and Trigonometry>Exercise 15.8>Q 1

The diagram represents a ramp $A B$ for a lifeboat. $A C$ is vertical and $C B$ is horizontal.

Calculate the length of $B C$ correct to $3$ significant figures. $(Take ∠ A B C = 16.2 °)$

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MEDIUM

Upper Secondary: IGCSE

IMPORTANT

Cambridge IGCSE® Mathematics Core and Extended Coursebook Second Edition>Chapter 15 - Scale Drawings, Bearings and Trigonometry>Exercise 15.8>Q 2

A B

is a chord of a circle with centre

O

, radius

8 cm

and

∠ A O B

= 120^{o}

.
Calculate the length of

A B

EASY

Upper Secondary: IGCSE

IMPORTANT

Cambridge IGCSE® Mathematics Core and Extended Coursebook Second Edition>Chapter 15 - Scale Drawings, Bearings and Trigonometry>Exercise 15.8>Q 3

The diagram represents a tent in the shape of a triangular prism. The front of the tent, $A B D$ , is an isosceles triangle with $A B = A D$ .

Question Image

The width $B D$ is $1.8 m$ and the supporting pole $A C$ is perpendicular to $B D$ and $1.5 m$ high. The tent is $3 m$ long. Calculate the angle between $A B and B D$ .

MEDIUM

Upper Secondary: IGCSE

IMPORTANT

Cambridge IGCSE® Mathematics Core and Extended Coursebook Second Edition>Chapter 15 - Scale Drawings, Bearings and Trigonometry>Exercise 15.8>Q 3

The diagram represents a tent in the shape of a triangular prism. The front of the tent, $A B D$ , is an isosceles triangle with $A B = A D$ .

Question Image

The width $B D$ is $1.8 m$ and the supporting pole $A C$ is perpendicular to $B D$ and $1.5 m$ high. The tent is $3 m$ long. Calculate the length of $A B$ .

EASY

Upper Secondary: IGCSE

IMPORTANT

Cambridge IGCSE® Mathematics Core and Extended Coursebook Second Edition>Chapter 15 - Scale Drawings, Bearings and Trigonometry>Exercise 15.8>Q 3

The diagram represents a tent in the shape of a triangular prism. The front of the tent, $A B D$ , is an isosceles triangle with $A B = A D$ .

Question Image

The width $B D$ is $1.8 m$ and the supporting pole $A C$ is perpendicular to $B D$ and $1.5 m$ high. The tent is $3 m$ long. Calculate the capacity inside the tent (i.e. volume).

MEDIUM

Upper Secondary: IGCSE

IMPORTANT

Cambridge IGCSE® Mathematics Core and Extended Coursebook Second Edition>Chapter 15 - Scale Drawings, Bearings and Trigonometry>Exercise 15.8>Q 4

Calculate the angles of an isosceles triangle that has sides of length $9 cm, 9 cm$ and $14 cm .$

Question Image

EASY

Upper Secondary: IGCSE

IMPORTANT

Cambridge IGCSE® Mathematics Core and Extended Coursebook Second Edition>Chapter 15 - Scale Drawings, Bearings and Trigonometry>Exercise 15.8>Q 5

The sketch represents a field $P Q R S$ on level ground. The sides $P Q$ and $S R$ run due east.
Write down the bearing of $S$ from $P$ .

Question Image

EASY

Upper Secondary: IGCSE

IMPORTANT

Cambridge IGCSE® Mathematics Core and Extended Coursebook Second Edition>Chapter 15 - Scale Drawings, Bearings and Trigonometry>Exercise 15.8>Q 5

The sketch represents a field $P Q R S$ on level ground. The sides $P Q$ and $S R$ run due east.
Calculate the shortest distance between $S R$ and $P Q$ . $(Take \sin 70 ° = 0.94)$

Question Image

The diagram represents a ramp AB for a lifeboat. AC is vertical and CB is horizontal. Calculate the size of ∠ABC correct to 1 decimal place.

Important Questions on Scale Drawings, Bearings and Trigonometry

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The diagram represents a ramp $A B$ for a lifeboat. $A C$ is vertical and $C B$ is horizontal.
Calculate the size of $∠ A B C$ correct to $1$ decimal place.