GCSE Maths · Higher · Chapter 22: Triangles · Lesson 3

Solving any triangle

Grades 6–8About 50 minutesCalculator allowed44 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
A right-angled triangle has hypotenuse 18 cm. The angle opposite side $x$ is $3 0^{\circ}$ . Find $x$ .
[1 mark]
Answer
A2
Last lesson
Find the other angle between $0^{\circ}$ and $18 0^{\circ}$ with the same sine as $4 0^{\circ}$ .
[1 mark]
Answer
A3
From chapter 6
The bearing of B from A is $23 5^{\circ}$ . Find the bearing of A from B.
[1 mark]
Answer
A4
From chapter 18
On a frequency polygon, the class $30 < x \leq 40$ with frequency 12 is plotted at which point?
[1 mark]
Answer

Grades 6–7

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

Example 1

Find $A C$ . Give your answer to 1 d.p.

Not drawn accurately

Hint

A C

is opposite the

3 9^{\circ}

angle and

B C

is opposite the

5 4^{\circ}

angle.

B1
Find $A C$ . Give your answer to 1 d.p.
[3 marks]
Not drawn accurately
Answer

Example 2

Find $A C$ . Give your answer to 1 d.p.

Not drawn accurately

Hint Two sides and the angle between them: use the cosine rule.

B2
Find $A C$ . Give your answer to 1 d.p.
[3 marks]
Not drawn accurately
Answer

Grades 6–8

C3
Find the area of triangle $A B C$ , to 1 d.p.
[2 marks]
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Answer
C4
The area of triangle $P QR$ is $84$ cm $^{2}$ . Find $P R$ , to 1 d.p.
[3 marks]
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Answer
C5
Find the area of the parallelogram $A B C D$ , to 1 d.p.
[2 marks]
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Answer
C6
Find the length of $A B$ , to 1 d.p.
[3 marks]
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Answer

Grades 7–8

D1
In triangle $A B C$ , $A B = 26$ cm, $B C = 17$ cm and angle $B A C = 3 5^{\circ}$ . Ella says, " $sin C = \frac{26 sin 3 5 ^{\circ}}{17}$ , so angle $A C B = 61. 3^{\circ}$ . There is only one possible triangle."
Explain why Ella is wrong. Give the other possible size of angle $A C B$ to 1 d.p.
[3 marks]
Answer

D2
A ship sails $14$ km from $A$ to $B$ on a bearing of $05 0^{\circ}$ , then $9$ km to $C$ on a bearing of $13 0^{\circ}$ .
Not drawn accurately
(a)
Show that angle $A B C = 10 0^{\circ}$ . Then work out $A C$ , to 1 d.p.
[3 marks]
Answer
(b)
Work out the bearing of $C$ from $A$ , to 1 d.p.
[3 marks]
Answer
Total for D2: 6 marks
D3
$A B C D$ is a quadrilateral field. Work out the size of angle $B C D$ , to 1 d.p.
[4 marks]
Not drawn accurately
Answer

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 choose the sine rule or the cosine rule.
I can find any side or angle of a triangle.
I can use $\frac{1}{2} ab sin C$ both ways.

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