Theory question 108
TrigonometryTwo observers Abu and Badu, 46 m apart, observe a bird on a vertical pole from the same side of the bird. The angles of elevation of the bird from Abu's and Badu's eye are 40° and 48° respectively. If at the foot of the pole, Abu and Badu are on the same horizontal: (a) illustrate the information in a diagram; (b) calculate, correct to one decimal place, the height of the pole.
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(a) Vertical pole with the bird on top; Abu and Badu on one horizontal line on the same side, Badu nearer the pole, 46 m apart; elevations 40° at Abu and 48° at Badu
(b) Let Badu be d m from the pole and h the height: h = d tan 48° = (d + 46) tan 40°
d(1.1106 − 0.8391) = 46 × 0.8391 ⇒ d ≈ 142.2 m
h = 142.16 × 1.1106 ≈ 157.9 m
The observer with the larger angle is nearer the pole.