Question

A ladder leans against the side of a house. The angle of elevation of the ladder is 68" when the bottom of the ladder is 16 it from the side of the house. Find the
length of the ladder. Round your answer to the nearest tenth
PLZ HELP ASAP!!!

Answer 1

Answer:

Length = 42.7 feet

Step-by-step explanation:

By considering it as right triangle we use trigonometric ratios to find the length of the ladder.

Given angle of elevation and adjacent side. We have to find the hypotenuse.

Trigonometric ratios

$sin \theta = \frac{Opposite}{hypotenuse}\\\\cos \theta = \frac{adjacent }{hypotenuse }\\\\Tan \theta = \frac{opposite}{adjacent}$                       $[ \ where \ \theta = 68^{ \circ} \ ]$

To find length of ladder ( or hypotenuse ) :

$cos \theta = \frac{16}{Length \ of \ ladder}\\\\Length \ of \ ladder = \frac{16}{cos 68} = 42.711$

Therefore, length of the ladder = 42.7 feet.