Question 94

- The angle of elevation of the top of a tower, vertically erected in the middle of a paddy field, from two points on a horizontal line through the foot of the tower are given to be α and β (α>β). The height of the tower is h unit. A possible distance (in the same unit) between the points is

Solution

In $$\triangle ABD$$,

$$\tan \alpha = \frac{h}{BD}$$

BD = $$hcot\alpha$$

In $$\triangle ACD,

$$tan\beta = \frac{h}{CD}$$

CD = $$hcot\beta$$

BC = BD + CD

= h($$cot\alpha + cot\beta$$)

So, the answer would be option d)$${h(cot\alpha+cot\beta)}$$

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