Question

What is X=? // which choice is correct ? (Ignore my guessing choice mark)

Answer 1

Given:

A figure of a right angle triangle.

To find:

The length of the shorter leg.

Solution:

In a right angle triangle,

$\tan\theta =\dfrac{Opposite}{Adjacent}$

In the given triangle,

$\tan (60^\circ) =\dfrac{18}{x}$

$\sqrt{3}=\dfrac{18}{x}$

$x=\dfrac{18}{\sqrt{3}}$

$x=\dfrac{18}{\sqrt{3}}\times \dfrac{\sqrt{3}}{\sqrt{3}}$

On further simplification, we get

$x=\dfrac{18\sqrt{3}}{3}$

$x=6\sqrt{3}$

$x=10.3923$

$x\approx 10.4$

Therefore, the length of the shortest leg is 10.4 and the correct option is B.