Edexcel IGCSE Math A 4.8.B right-triangle trigonometry

Practise right-triangle trigonometry by labelling opposite, adjacent and hypotenuse sides, then choosing sin, cos or tan.

Exam points

Choose sine, cosine or tangent after labelling sides relative to the angle.
Calculate a missing length or angle and round to the requested accuracy.
Combine trigonometry with circle or multi-step diagram information when required.

[Maximum number: 4]

28 A B C is a right-angled triangle.

Diagram NOT accurately drawn

$A C=21 \mathrm{~cm} \quad B C=15 \mathrm{~cm} \quad$ angle $A B C=90^{\circ}$
The point D lies on AB such that $D B=9 \mathrm{~cm}$
Work out the size of angle ACD
Give your answer correct to one decimal place.

$\angle ACB=\cos^{-1}\left(\frac{15}{21}\right)=44.4\ldots^\circ$ $\angle DCB=\tan^{-1}\left(\frac{9}{15}\right)=30.9\ldots^\circ$ $\angle ACD=44.4\ldots^\circ-30.9\ldots^\circ=13.5\ldots^\circ$

Final answer:
$13.5^\circ$

Accept $13.4^\circ$ to $13.6^\circ$ .

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4.8.B Trigonometry in right-angled triangles question 1