CAIE IGCSE Mathematics Core C6.2.1 Know and Use the Sine Cosine and Tangent Ratios for Acute Angles in Questions

Practise right-triangle trigonometry by identifying the relevant sides, setting up a ratio and calculating a missing length or acute angle with clear working.

Exam points

Use a sine ratio to calculate a missing side from an acute angle and the hypotenuse.
Read the legs from a square grid and use an inverse ratio to find the requested acute angle.
Calculate a perpendicular height with a ratio, using half the base in an isosceles triangle.
Show a trigonometric equation and an unrounded value to justify the stated accuracy.

[Maximum number: 7]

(a)

NOT TO SCALE

ABC is a right-angled triangle.

Calculate BC.
$BC=\quad\mathrm{cm}$

[ 3 ]

8.4
M2 for $9.1^2-3.5^2$ oe or better
or M1 for $BC^2+3.5^2=9.1^2$ oe or better

(b)

$\triangle E F$ is a right-angled triangle.

Calculate EF.

E F=\ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots . . . c m ~[2]

[ 2 ]

6.88 to 6.881

2

M1 for $\cos 35=\frac{[\ldots]}{8.4}$ oe or better
or $\sin 55=\frac{[\ldots]}{8.4}$ oe or better

(c)

JKL is a right-angled triangle.

NOT TO SCALE

Calculate angle JKL.

[ 2 ]

$51.3[4 \ldots]$

2

M1 for $\tan [\ldots=] \frac{10}{8}$ oe or better

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CAIE IGCSE Mathematics Core C6.2.1 Know and Use the Sine Cosine and Tangent Ratios for Acute Angles in Questions question 1

Question (a)

Question (b)

Question (c)