Question

In the given fig. $\angle DAB$ = $\angle ABC$ = ${90}^{\circ }$. Also if $\alpha$ + $\phi$ = ${90}^{\circ }$ and α = 2$\phi$. Find the ratio of H and h.

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Answer 1

$\alpha$ + $\phi$ = ${90}^{\circ }$ --------------------- I

$\alpha$ = 2$\phi$ --------------------- II

Solving I and II, we get $\alpha$ = ${60}^{\circ }$ and $\phi$ = ${30}^{\circ }$

Let length of base AB be x

In $\Delta ABC$, $\tan$${60}^{\circ }$ = $\frac{H}{x}$

and $\Delta ABD$, $\tan$${30}^{\circ }$ = $\frac{h}{x}$

$\Rightarrow$ $\frac{H}{h}$ = 3