Question 103

The angles of elevation of a pole from two points which are 75 m and 48 m away from its base are $$\alpha$$ and $$\beta$$, respectively. If $$\alpha$$ and $$\beta$$ are complementary, then the height of the tower is:

Solution

$$\angle \alpha +\angle \beta = 90\degree$$ (complementary angle)

OA = 48 m

OB = 75 m

$$tan\beta = \frac{OP}{OA}$$

$$tan\beta = \frac{OP}{48}$$

$$tan\alpha = \frac{OP}{75}$$

$$tan(90 - \beta) = \frac{OP}{75}$$

$$cot\beta = \frac{OP}{75}$$

$$tan\beta = \frac{1}{cot\beta}$$

$$\frac{OP}{48} = \frac{75}{OP}$$

OP = $$\sqrt{75 \times 48} = \sqrt{3600}$$ = 60 m

The height of tower is 60 m.

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