A point H is 20 m away from the foot of a tower on the same horizontal ground. From the point H, the angle of elevation of the point P on the tower and the top (T) of the tower are 30° and 50° respectively. Calculate, correct to 3 significant figures :
(a) /PT/; (b) the distance between H and the top of the tower
(c) The position of H if the angle of depression of H from the top of the tower is to be 40°.
Explanation
(a) (tan 50° = frac{|TF|}{20} implies |TF| = 20 tan 50)
= (20 times 1.1918)
= (23.836 m)
(tan 30 = frac{|PF|}{20} implies |PF| = 20 tan 30)
= (20 times 0.5774)
= (11.548 m)
(therefore |PT| = 23.836 m – 11.548m)
= (12.288 m approxeq 12.3 m)
(b) (|TH| = frac{20}{cos 50})
= (frac{20}{0.6428})
= (31.11 m)
(c) (|HF| = frac{20 tan 50°}{tan 40°})
= (frac{20 times 1.1918}{0.8391})
= (28.41 m)