Theory question 103
Trigonometry(a) The angle of depression of a point P on the ground from the top T of a building is 23.6°. If the distance from P to the foot of the building is 50 m, calculate, correct to the nearest metre, the height of the building.
(b) In the diagram, PT//SU, QS//TR, |SR| = 6cm and |RU| = 10cm. If the area of ΔTRU = 45cm2, calculate the area of trapezium QTUS.
Show the model answer
Model answer
(a) Angle of elevation of T from P = 23.6°; h = 50 tan 23.6° ≈ 21.8 ≈ 22 m
(b) Area of ΔTRU = ½ × 10 × h = 45 → height h = 9 cm
QSRT is a parallelogram, so |QT| = |SR| = 6 cm; |SU| = 6 + 10 = 16 cm
Area of QTUS = ½(6 + 16) × 9 = 99 cm²
Explanation
The triangle and the trapezium have the same height.