Questions: A 9 - ft ladder leans against the side of a house. How far is the bottom of the ladder from the side of the house when the angle of elevation of the ladder is 62 degrees? Round your answer to the nearest tenth.

A 9 - ft ladder leans against the side of a house. How far is the bottom of the ladder from the side of the house when the angle of elevation of the ladder is 62 degrees?

Round your answer to the nearest tenth.

Transcript text: A 9 - ft ladder leans against the side of a house. How far is the bottom of the ladder from the side of the house when the angle of elevation of the ladder is $62^{\circ}$ ? Round your answer to the nearest tenth.

Solution

Solution Steps

Step 1: Identify the given values

Ladder length (hypotenuse) = 9 ft
Angle of elevation = 62°

Step 2: Determine the trigonometric function to use

To find the distance from the bottom of the ladder to the side of the house (adjacent side), we use the cosine function: \[ \cos(\theta) = \frac{\text{adjacent}}{\text{hypotenuse}} \]

Step 3: Set up the equation

\[ \cos(62°) = \frac{\text{adjacent}}{9} \]

Step 4: Solve for the adjacent side

\[ \text{adjacent} = 9 \times \cos(62°) \]

Step 5: Calculate the value

Using a calculator: \[ \cos(62°) \approx 0.4695 \] \[ \text{adjacent} = 9 \times 0.4695 \approx 4.2255 \]