a 14 ft ladder leans against the side of a house. the bottom of the ladder is 5 ft away from the side of the…

a 14 ft ladder leans against the side of a house. the bottom of the ladder is 5 ft away from the side of the house. find x, the angle of elevation of the ladder. round your answer to the nearest tenth of a degree.

a 14 ft ladder leans against the side of a house. the bottom of the ladder is 5 ft away from the side of the house. find x, the angle of elevation of the ladder. round your answer to the nearest tenth of a degree.

Answer

Explanation:

Step1: Identify the triangle type

This is a right triangle, with hypotenuse (ladder) = 14 ft, adjacent side (distance from house) = 5 ft. We use cosine: $\cos(x) = \frac{\text{adjacent}}{\text{hypotenuse}} = \frac{5}{14}$.

Step2: Solve for x

Take the arccosine: $x = \arccos\left(\frac{5}{14}\right)$. Calculate this value. Using a calculator, $\arccos\left(\frac{5}{14}\right) \approx 69.1^\circ$.

Answer:

$x \approx 69.1^\circ$