GCSE Maths · Higher · Chapter 11: Right-angled triangles · Lesson 4

Trigonometry in context

Grades 5–8About 50 minutesCalculator allowed37 marks

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NameClassDate

Do Now

Grades 4–6

The first question is what today's lesson needs. The others bring back earlier topics.

A1
Needed today
Write down the exact value of $cos 6 0^{\circ}$ .
[1 mark]
Answer
A2
From chapter 8
Expand and simplify $4 (x + 4) + 3 (x - 5)$ .
[1 mark]
Answer
A3
From chapter 8
Expand $(3 x - 5) (x - 2)$ .
[1 mark]
Answer
A4
From chapter 3
A pie chart shows 60 people. A sector has angle $12 0^{\circ}$ . How many people is that?
[1 mark]
Answer

Grades 5–6

Your teacher works through each example with you. Then try the one beside it.

Example 1

From 60 m away on level ground, the angle of elevation of the top of a tree is $3 1^{\circ}$ . Work out its height $h$ , to 1 d.p.

Not drawn accurately

Hint Measure up from the horizontal:

h

is opposite, 60 m adjacent.

B1
From the top of a 38 m lighthouse, the angle of depression of a boat is $1 4^{\circ}$ . Work out the distance $d$ to the boat, to 1 d.p.
[3 marks]
Not drawn accurately
Answer

Example 2

An isosceles triangle has two equal sides of 17 cm and a base of 24 cm. Work out the base angle $θ$ , to 1 d.p.

Not drawn accurately

Hint The height cuts the base in half: hypotenuse 17 cm, base 12 cm.

B2
An isosceles triangle has equal sides of 11 cm with $7 2^{\circ}$ between them. Work out its base $x$ , to 1 d.p.
[3 marks]
Not drawn accurately
Answer

Grades 5–7

C1
Ravi's eyes are 1.6 m above level ground. He stands 24 m from the foot of a flagpole 13.6 m tall. Work out the angle of elevation $θ$ of the top of the flagpole from his eyes, to 1 decimal place.
[3 marks]
Not drawn accurately
Answer
C2
A walker goes 5.4 km due east from her start, then 3.9 km due south to her finish. Work out the bearing of her finish from her start, to the nearest degree.
[3 marks]
Not drawn accurately
Answer

C3
An isosceles triangle has two equal sides of 13 cm and two base angles of $6 4^{\circ}$ . Work out the area of the triangle, to 3 significant figures.
[4 marks]
Not drawn accurately
Answer
C4
A rhombus has diagonals of 16 cm and 10 cm. Work out the size of each obtuse angle of the rhombus, to 1 decimal place.
[3 marks]
Not drawn accurately
Answer

Grades 6–8

D1
From a boat, the angle of elevation of the top of a vertical cliff is $4 1^{\circ}$ . Tom says, "So the angle of depression of the boat from the top of the cliff is $4 9^{\circ}$ ."
Explain why Tom is wrong, and give the correct angle.
[2 marks]

Grade 8 and beyond

No route is given. The hints are at the end of the sheet. Use one at a time.

Colour one circle on each line.

	Not yet	Nearly	Yes
I can use elevation and depression.
I can solve bearing journeys.
I can halve an isosceles triangle.

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