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Trigonometric Ratios and Identities · Paper 2 — Free Maths AI HL Practice Questions

1MasterySAQ-SDefinitions of sine, cosine and tangent using right-angled triangles9 marksPaper 2~14 min

A surveyor measures the height of a vertical cliff face. From a point

P

on level ground, the angle of elevation to the top of the cliff

C

32^\circ

. The surveyor walks

50\,\text{m}

directly towards the cliff to a point

Q

. From

Q

, the angle of elevation to

C

48^\circ

. Let

h

metres be the height of the cliff and

x

metres be the horizontal distance from

Q

to the base of the cliff

B

(a)

Write down an expression for

h

in terms of

x

and

\tan 48^\circ

. [1 mark]

(b)

Using your answer to part (a) and the angle of elevation from

P

, form an equation in

x

alone and hence show that

x = \frac{50\tan 32^\circ}{\tan 48^\circ - \tan 32^\circ}

[3 marks]

(c)

Calculate the height of the cliff

h

, correct to 3 significant figures. [1 mark]

(d)

The surveyor estimates that each angle of elevation could have a measurement error of up to

\pm 1^\circ

. Determine the maximum possible value of

h

under this error, and hence evaluate whether the measurement error has a significant effect on the calculated height. [4 marks]

Solutions

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