Theory question 105
Mensuration of Plane Shapes(a) In the diagram, PQST is a parallelogram, PQR is a straight line, |TS| = 8 cm, |SM| = 6 cm and area of triangle PSR = 36 cm2. 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 angles of 45° and 60° respectively. If the tree is 10.65 m high, calculate, correct to 3 significant figures, the height of the flagpole.
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(a) Area of triangle PSR = ½ × |PR| × 6 = 36 → |PR| = 12 cm
|PQ| = |TS| = 8 cm (opposite sides of parallelogram), so |QR| = 12 − 8 = 4 cm
(b) Horizontal distance d = 10.65/tan 60° ≈ 6.149 m
Drop from the bird to the top of the pole = d tan 45° ≈ 6.149 m
Height of flagpole = 10.65 − 6.149 ≈ 4.50 m
Use the 60° angle (to the bottom) to find the horizontal distance first.