Edexcel IGCSE Math B 9.A sine cosine and tangent

Practise trig-ratio questions by labelling opposite, adjacent and hypotenuse sides, then selecting the correct ratio for the diagram.

Exam points

Choose sine, cosine or tangent after labelling sides relative to the angle.
Calculate missing lengths or angles and round to the requested accuracy.
Use perpendicular lines or framework diagrams to create the right triangle needed.

[Maximum number: 3]

Diagram NOT accurately drawn

Figure 3 shows a circle with centre O and radius 10 cm.
The points A and B lie on the circle such that $\angle A O B=100^{\circ}$ The point C is such that AC and BC are tangents to the circle.

Calculate the length, in cm to 3 significant figures, of BC.

One correct method:
$\tan40^\circ=\frac{10}{BC}$
Equivalently:
$\tan50^\circ=\frac{BC}{10}$
Hence:
$BC=10\tan50^\circ=11.9175\ldots$
Final answer:
$11.9\text{ cm}$

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9.A Sine, cosine and tangent question 1