Theory question 105
TrigonometryA boy stands at a point M on the same horizontal level as the foot, T, of a vertical building. He observes an object on the top, P of the building at an angle of elevation of 66°. He moves directly backwards to a new point C and observes the same object at an angle of elevation of 53°. If |MT| = 50 m:
(a) illustrate the information in a diagram;
(b) calculate, correct to one decimal place: (i) the height of the building; (ii) |MC|
Show the model answer
Model answer
(a) Vertical PT with right angle at T; C, M, T in a straight line with MT = 50 m; angle of elevation 66° at M and 53° at C
(b)(i) PT = 50 tan 66° ≈ 112.3 m
(ii) CT = 112.30 ÷ tan 53° ≈ 84.63 m, so |MC| = 84.63 − 50 ≈ 34.6 m
Explanation
C is further from the building than M, so the smaller angle is at C.