If a flagstaff of 6 m high placed on the top | vedclass

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(A) Let $h$ be the height of the tower and $x$ be the length of its shadow. The flagstaff of height $6 \ m$ is placed on top of the tower.From the geo

Vedclass · Accepted Answer

$60$

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(A) Let $h$ be the height of the tower and $x$ be the length of its shadow. The flagstaff of height $6 \ m$ is placed on top of the tower.From the geometry of the problem,we have two similar triangles $AEC$ and $BDC$ as shown in the figure.For the tower of height $h$ and shadow $x$,we have $	an 	heta = \frac{h}{x}$.For the combined height $(h + 6)$ and total shadow $(x + 2\sqrt{3})$,we have $	an 	heta = \frac{h + 6}{x + 2\sqrt{3}}$.Equating the two expressions for $	an 	heta$:$\frac{h}{x} = \frac{h + 6}{x + 2\sqrt{3}}$$h(x + 2\sqrt{3}) = x(h + 6)$$hx + 2\sqrt{3}h = xh + 6x$$2\sqrt{3}h = 6x$$\frac{h}{x} = \frac{6}{2\sqrt{3}} = \frac{3}{\sqrt{3}} = \sqrt{3}$Since $	an 	heta = \frac{h}{x} = \sqrt{3}$,we have $	heta = 60^o$.

If a flagstaff of $6 \ m$ high placed on the top of a tower throws a shadow of $2\sqrt{3} \ m$ along the ground,then the angle (in degrees) that the sun makes with the ground is.......$^o$

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