(a) If (cos alpha = 0.6717), use mathematical tables to find (i) (alpha) ; (ii) (sin alpha)
(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 of P from the foot of the building is 50m, calculate the height of the building, correct to the nearest metre.
Explanation
(a) (i) Given (cos alpha = 0.6717)
(alpha = cos^{-1} 0.6717 = 47.8°)
(From cosine of angle table)
(ii) (sin 47.8° = 0.7408)
(b)
From the diagram, (< BPT = < PTR = 23.6°)
(therefore |BT| = |BP| tan 23.6°)
= (50 tan 23.6° = 50 times 0.4369)
= (21.8469 m)
(therefore) The height of the building = 22m (to the nearest metre).