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: 3]

A zip wire is shown as the dashed line AC in the diagram.

Diagram NOT accurately drawn

The zip wire is supported by two vertical posts AB and CD standing on horizontal ground.

C D=2.6 \mathrm{~m} \quad B D=12 \mathrm{~m}

The zip wire makes an angle x with the horizontal, as shown in the diagram. The design of the zip wire requires the angle x to be at least $5^{\circ}$

Work out the least possible height of the post AB
Give your answer correct to 3 significant figures.

Required vertical rise for $5^\circ$ :
$12\tan5^\circ=1.04986\ldots$
Minimum height:
$AB=2.6+1.04986\ldots=3.64986\ldots$
Final answer:
3.65
Accept answers that round to 3.65.

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4.8.B Trigonometry in right-angled triangles question 1