Theory question 105
TrigonometryThe feet of two vertical poles of height 3m and 7m are in line with a point P on the ground, the smaller pole being between the taller pole and P and at a distance of 20m from P. The angle of elevation of the top (T) of the taller pole from the top (R) of the smaller pole is 30°. Calculate the: (i) distance RT; (ii) distance of the foot of the taller pole from P, correct to three significant figures; (iii) angle of elevation of T from P, correct to one decimal place.
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Height of T above R = 7 − 3 = 4m
(i) sin 30° = 4/RT, so RT = 4/0.5 = 8m
(ii) Distance between the poles = 4/tan 30° = 6.928m; distance from P = 20 + 6.928 = 26.9m
(iii) tan θ = 7/26.93 = 0.2600, θ = 14.6°
Draw the horizontal through R; the right-angled triangle above it has height 4m.