Question

A $25$-foot ladder stands against a vertical wall at an angle of n degrees with the ground. If $\sin n=\frac{4}{5}$, how far is the base of the ladder from the wall?

• A. $12$
• B. $13$
• C. $14$
• D. $15$
• E. $16$

Answer 1

The correct option is D $15$

A $25$ foot ladder stands against a vertical wall forming $n$ degrees.
So hypotenuse will be $25$
Given, $\sin n=\frac{4}{5}$
We know, $\sin n=\frac{perpendicular}{hypotenuse}$
Let perpendicular be $x$
$\Rightarrow \frac{4}{5}=\frac{x}{25}$
$\Rightarrow 5x=100$
$\Rightarrow x=20$
Let the base be $y$
As per Pythagoras theorem, we have

hypotenuse${}^2=$ base${}^2+$ perpendicular${}^2$
$\Rightarrow {25}^2=y^2+{20}^2$
$\Rightarrow y^2={25}^2-{20}^2$
$\Rightarrow y^2=625-400$
$\Rightarrow y^2=225$
$\Rightarrow y=15$
Base of the ladder is $15$ foot from the wall.