Question

A vertical post $15$ ft high is broken at a certain height and its upper part, not completely separated, meets the ground at an angle of ${30}^{\circ }$. Find the height at which the post is broken.

• A. $10ft$
• B. $5ft$
• C. $15\sqrt{3}(2-\sqrt{3})ft$
• D. $5\sqrt{3}ft$

Answer 1

The correct option is B $5ft$

Given that, $AB=Post=15feet,\angle CDB={30}^{\circ }$ and the post breaks at point $C$.
Let the height at which post is broken be $x$ feet.
$\Rightarrow AC=CD=(15-x)feet$
From $△BCD$,
$\sin {30}^{\circ }=\frac{BC}{CD}$
$\Rightarrow \frac{1}{2}=\frac{x}{15-x}\Rightarrow 2x=15-x\Rightarrow 3x=15\Rightarrow x=5$ feet
Hence, the height at which the post is broken is $5$ feet.