Question

A 10 ft ladder is resting against the wall. The ladder touches the ground 6ft away from the wall. What angle rounded to the nearest tenth is the bottom of the ladder making with the ground

Answer 1

ANSWER

$53.1 \degree$

EXPLANATION

Let

$x$
be the angle the bottom of the ladder makes with the ground.

See attachment.

Then

$\cos(x) = \frac{adjacent}{hypotenuse}$

$\cos(x) = \frac{6}{10}$

$\cos(x) = 0.6$

We take the cosine inverse if both sides to obtain,

$x= \cos ^{ - 1} (0.6)$

$x = 53.130$

To the nearest tenth is 53.1°