Question

8. Two observers Abu and Badu, 46m apart, observe a board 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.

Accepted Answer

(a) Let the height of the pole (to the board) be h. Since Badu's angle of elevation (48°) is greater than Abu's (40°), Badu is closer to the pole. Let Badu's horizontal distance from the foot of the pole = d, so Abu's distance = d+46 (Abu being further away). A simple diagram would show: the pole standing vertically at one end, with Badu at distance d from its foot and Abu at distance (d+46) from its foot, both on the same horizontal line, with lines of sight rising at 48° (from Badu) and 40° (from Abu) to the top of the pole.

(b) tan48° = h/d → d = h/tan48°
tan40° = h/(d+46) → d+46 = h/tan40°
Subtracting: h/tan40° − h/tan48° = 46
h(1/tan40° − 1/tan48°) = 46
h(1.1918 − 0.9004) = 46
h(0.2914) = 46
h = 46/0.2914 ≈ 157.9m (correct to one decimal place).

NABTEB Mathematics 2024 Theory — Question 8

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