The height of a tower is 50 , m and the heigh | vedclass

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Question

(B) Let the distance between the base of the tower and the midpoint be $a$,and the distance between the base of the building and the midpoint be $a$.I

Vedclass · Accepted Answer

$\alpha > \beta$

Vedclass · Answer

(B) Let the distance between the base of the tower and the midpoint be $a$,and the distance between the base of the building and the midpoint be $a$.In the right-angled triangle formed by the tower,we have $	an \alpha = \frac{50}{a}$.In the right-angled triangle formed by the building,we have $	an \beta = \frac{30}{a}$.Taking the ratio,we get $\frac{	an \alpha}{	an \beta} = \frac{50/a}{30/a} = \frac{50}{30} = \frac{5}{3}$.Since $\frac{5}{3} > 1$,it follows that $	an \alpha > 	an \beta$.Since the tangent function is strictly increasing in the interval $(0, 90^\circ)$,$	an \alpha > 	an \beta$ implies $\alpha > \beta$.

The height of a tower is $50 \, m$ and the height of a building is $30 \, m$. Watching from the midpoint of the line segment joining their bases,the angle of elevation of the top of the tower is $\alpha$ and that of the building is $\beta$. Then,which of the following holds true?

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