Theory question 108
TrigonometryA point H is 20 m away from the foot of a tower on the same horizontal ground. From the point H, the angle of elevation of the point (P) on the tower and the top (T) of the tower are 30° and 50° respectively. Calculate, correct to 3 significant figures: (a) |PT|; (b) the distance between H and the top of the tower; (c) the position of H if the angle of depression of H from the top of the tower is to be 40°.
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Model answer
(a) Height of T = 20 tan 50° = 23.84 m; height of P = 20 tan 30° = 11.55 m. |PT| = 12.3 m.
(b) |HT| = 20/cos 50° ≈ 31.1 m.
(c) New distance from the foot = 23.84/tan 40° ≈ 28.4 m, i.e. H must move about 8.41 m further away from the tower.
Explanation
The angle of depression from T equals the angle of elevation from H.