Theory question 102
Trigonometry(a) The angle of depression of a boat from the mid-point of a vertical cliff is 35°. If the boat is 120 m from the foot of the cliff, calculate the height of the cliff.
(b) Towns P and Q are x km apart. Two motorists set out at the same time from P to Q at steady speeds of 60 km/h and 80 km/h. The faster motorist got to Q 30 minutes earlier than the other. Find the value of x.
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Model answer
(a) Height of the mid-point = 120 tan 35° = 120 × 0.7002 ≈ 84.0 m. Height of cliff = 2 × 84.02 ≈ 168 m.
(b) x/60 − x/80 = ½ (30 minutes). (4x − 3x)/240 = ½, so x = 120 km.
Explanation
The angle of depression equals the angle of elevation from the boat.