On a straight line passing through the foot of a tower, two points C and D

Trigonometry (10)

On a straight line passing through the foot of a tower, two points C and D are at distances of 4 m and 16 m from the foot respectively. If the angles of elevation from C and D of the top of the tower are complementary, then find the height of the tower. 

Answer

$$ \text{tan} $\theta = \frac{h}{4} $$

$$ \text{tan} (90 - \theta) = \frac{h}{16} $$

$$ \text{cot} \theta = \frac{h}{16} $$

Solving (i) and (ii) to get

h² = 64

h = 8 m

• Exam Year: 2017