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# The length of the shadow of a pillar is increased by 60m when the angle of elevation of the sun becomes 30^@ from 45^@. Find the height of the pillar ?

## The length of the shadow of a pillar is increased by $60 m$ when the angle of elevation of the sun becomes ${30}^{\circ}$ from ${45}^{\circ}$. Find the height of the pillar ?

Jun 25, 2018

#### Answer:

height=81.967 metre(approx.)

#### Explanation:

we have $\tan 45 = \frac{x}{x}$
and $\tan 30 = \frac{x}{x} + 60$
$\implies \frac{1}{\sqrt{3}} = \frac{x}{x} + 60$................tan30=$\frac{1}{\sqrt{3}}$
$\implies x + 60 = \sqrt{3} \cdot x$
x(sqrt3-1)=60; => x(0.732)=60 ;=> x~81.967 m
hence height =81.967 metre