(a) The angles of depression of the top and bottom of a building are 51° and 62° respectively from the top of a tower 72m high. The base of the building is on the same horizontal level as the foot of the tower. Calculate the height of the building correct to 2 significant figures. (b) In the diagram, PR is a chord of the circle centre O and radius 30cm, < POR = 120°. Calculate correct to three significant figures : (i) the length of chord PR ; (ii) the length of arc PQR ; (iii) the perimeter of the shaded portion. (Take ).
Explanation
(a) ST = QR ; PS = height of tower. In PST, = 38.283m 38.3m In PQR, = = QS = RT (height of the building) QS = PS - PQ = 72 - 47.3 = 24.7m (b) (i) (isosceles triangle) = PT = TR PR = 2PT = = (ii) Length of minor arc, PQR = = = (iii) Perimeter of shaded portion = chord PR + Arc PQR = 51.96 + 62.84 = 114.8 cm 115cm.
