GCSE Maths · Higher · Chapter 11: Right-angled triangles · Lesson 3

Trigonometric ratios

Grades 5–8About 45 minutesCalculator allowed36 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 13 cm and one side 5 cm. Find the other side.
[1 mark]
Answer
A2
Last lesson
A cuboid is 6 cm by 6 cm by 7 cm. Find the length of its longest diagonal.
[1 mark]
Answer
A3
From chapter 1
Find the highest common factor of $30$ and $45$ .
[1 mark]
Answer
A4
From chapter 7
Enlarge $(3, - 3)$ by scale factor 3, centre the origin.
[1 mark]
Answer

Grades 5–6

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

Example 1

Work out the length $x$ . Give your answer to 1 decimal place.

Not drawn accurately

Hint The unknown is underneath the fraction line, so divide by the ratio.

B1
Work out the length $x$ . Give your answer to 1 decimal place.
[3 marks]
Not drawn accurately
Answer

Example 2

Work out the size of angle $θ$ . Give your answer to 1 decimal place.

Not drawn accurately

Hint You know the opposite and the hypotenuse, so use

sin^{- 1}

B2
Work out the size of angle $θ$ . Give your answer to 1 decimal place.
[2 marks]
Not drawn accurately
Answer

Grades 5–7

C1
$P S R$ is a straight line. Work out the length $x$ , to 1 d.p.
[3 marks]
Not drawn accurately
Answer
C2
Work out the area of the triangle, to 3 significant figures.
[3 marks]
Not drawn accurately
Answer

C3
The line $A B$ joins $A (1, 2)$ and $B (7, 6)$ . Work out the angle $θ$ between $A B$ and the horizontal, to 1 d.p.
[3 marks]
Not drawn accurately
Answer
C4
$A B C D$ is a trapezium. $A B$ is parallel to $D C$ and angle $D A B = 9 0^{\circ}$ . $A B = 12.4$ cm, $A D = 6.5$ cm and angle $A B C = 5 8^{\circ}$ . Work out the perimeter of $A B C D$ . Give your answer to 3 significant figures.
[5 marks]
Not drawn accurately
Answer

Grades 6–8

D1
Sam says, " $tan 4 0^{\circ}$ is twice $tan 2 0^{\circ}$ , because $4 0^{\circ}$ is twice $2 0^{\circ}$ ."
Show that Sam is wrong.
[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 name the opposite, adjacent and hypotenuse and choose the right ratio.
I can find a side whether it is above or below the fraction line.
I can find an angle from two sides.

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