Question

5(a) In the diagram above, PQST is a parallelogram, PR is a straight line, |TS|=8cm, |SM|=6cm and area of triangle PSR=36cm². Find the value of |QR|.
(b) A tree and a flagpole are on the same horizontal ground. A bird on top of the tree observes the top and bottom of the flagpole below it at angle of 45° and 60° respectively. If the tree is 10.65m high, calculate correct to 3 significant figures, the height of the flagpole.

Accepted Answer

(a) Area of triangle PSR = ½×base×height = ½×|PR|×|SM|
36 = ½×|PR|×6 → |PR|=12cm
Since PQST is a parallelogram with |TS|=8cm=|PQ|, and PR is a straight line through Q,
|QR| = |PR|-|PQ| = 12-8 = 4cm

(b) Let height of flagpole = h, height of tree = 10.65m, horizontal distance = x
From the two angles of depression (45° and 60°) to top and bottom of flagpole:
tan60° = 10.65/x → x = 10.65/tan60° = 6.15m
tan45° = (10.65-h)/x → 10.65-h = x×tan45° = 6.15
h = 10.65-6.15 = 4.5m (≈4.50m to 3 s.f.)

WAEC Mathematics 2016 Theory — Question 5

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