Theory question 105
Trigonometry(a) If cos α = 0.6717, use Mathematical Table to find: (i) α (ii) sin α (b) 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 cm, calculate the height of the building, correct to the nearest metre.
Show the model answer
Model answer
(a)(i) α = 47.8°
(ii) sin α = sin 47.8° = 0.7408
(b) The angle of elevation of T from P = 23.6° (alternate angles).
Height = 50 tan 23.6° = 50 × 0.4369 = 21.8 ≈ 22 m.
Explanation
The angle of depression from T equals the angle of elevation from P.