CAIE IGCSE Mathematics Extended Sine Cosine and Tangent

Use SOHCAHTOA to select and rearrange sine, cosine or tangent for a right-angled triangle, calculate a missing side or acute angle, and round only the final result.

Exam points

label the sides relative to the target acute angle and select sine, cosine or tangent
rearrange the chosen ratio to calculate a side or use its inverse to calculate the angle
show the unrounded calculator value before rounding to the stated decimal places or significant figures

[Maximum number: 4]

NOT TO SCALE

The diagram shows a field, ABCD with B north of A.
BD is a path across the field.
$A B=85 \mathrm{~m}, A D=72 \mathrm{~m}, B D=129 \mathrm{~m}$ , angle $B D C=39^{\circ}$ and angle $B C D=60^{\circ}$ .

Show that angle $A B D=31.6^{\circ}$ , correct to 1 decimal place.

$[\cos=]\frac{85^2+129^2-72^2}{2\times85\times129}$
M2
M1 for $72^2=85^2+129^2-2\times85\times129\cos ABD$ $31.58\ldots$
A2
A1 for 0.851 to 0.852 or $\frac{9341}{10965}$ or equivalent fraction

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E6.2.1 Know and use the sine, cosine and tangent ratios for acute angles in question 1