Questions: A 16 ft ladder leans against the side of a house. The bottom of the ladder is 9 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. x=

A 16 ft ladder leans against the side of a house. The bottom of the ladder is 9 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.
x=

Transcript text: A 16 ft ladder leans against the side of a house. The bottom of the ladder is 9 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. \[ x= \]

Solution

Solution Steps

Step 1: Identify the given values

The problem provides the length of the ladder (hypotenuse) as 16 feet and the distance from the bottom of the ladder to the house (adjacent side) as 9 feet.

Step 2: Set up the trigonometric function

To find the angle of elevation $ x $, we use the cosine function, which relates the adjacent side and the hypotenuse in a right triangle: \[ \cos(x) = \frac{\text{adjacent}}{\text{hypotenuse}} \] \[ \cos(x) = \frac{9}{16} \]

Step 3: Solve for the angle $ x $

Use the inverse cosine function to find $ x $: \[ x = \cos^{-1}\left(\frac{9}{16}\right) \]

Step 4: Calculate the angle

Using a calculator: \[ x \approx \cos^{-1}(0.5625) \] \[ x \approx 55.2^\circ \]