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

1MasterySAQ-SDefinitions of sine, cosine and tangent using right-angled triangles6 marksPaper 2~9 min
A surveyor measures the height of a vertical cliff face. From point PP on level ground, 50 m50\,\text{m} from the base of the cliff BB, the angle of elevation to the top of the cliff TT is 35°35°. The surveyor then moves a further 30 m30\,\text{m} directly away from the cliff to point QQ.
(a)
Calculate the height of the cliff h=BTh = BT, giving your answer correct to 3 significant figures. [2 marks]
(b)
Calculate the angle of elevation from QQ to TT, giving your answer to the nearest degree. [2 marks]
(c)
The surveyor claims that the angle ∠TPQ\angle TPQ (the angle at PP in triangle TPQTPQ, where TT is the cliff top) is greater than 10°10°. Determine whether this claim is correct, showing all working. [2 marks]
diagram

Solutions

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