A vertical tower stands on a horizontal plane and is surmounted by a vertical flag-staff of height $6$ m. At a point on the plane, the angle of elevation of the bottom and top of the flag-staff are $3

Question

A vertical tower stands on a horizontal plane and is surmounted by a vertical flag-staff of height $6$ m. At a point on the plane, the angle of elevation of the bottom and top of the flag-staff are $30°$ and $45°$ respectively. Find the height of the tower. (Take $\sqrt{3} = 1.73$)

Accepted Answer

Step 1: Right triangle with tower BC of height h, flagstaff AB of 6m on top, point D on ground. Angles 45° and 30° at D.
Step 2: Let height of tower $= h$ m, $CD = x$ m.
$\frac{h}{x} = 	an 30° \Rightarrow x = h\sqrt{3}$
$\frac{6+h}{x} = 	an 45° \Rightarrow 6 + h = x$
Step 3: $	herefore h = \frac{6}{\sqrt{3} - 1} = \frac{6(\sqrt{3}+1)}{2} = 3(\sqrt{3}+1) = 3 	imes 2.73 = 8.19$ m

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