Questions: QUESTION 10 A 25 foot ladder makes an angle of 30 degrees with the ground. How far is the bottom of the ladder from the wall? 14.4 feet

Solution Steps

To find how far the bottom of the ladder is from the wall, we can use trigonometry. Specifically, we can use the cosine function, which relates the adjacent side (distance from the wall) to the hypotenuse (length of the ladder) in a right triangle. The formula is: adjacent = hypotenuse * cos(angle).

We are given a ladder of length 25 feet that makes an angle of 30 degrees with the ground. This forms a right triangle where the ladder is the hypotenuse, the distance from the wall is the adjacent side, and the angle with the ground is 30 degrees.

To find the distance from the wall, we use the cosine function, which is defined as: \[ \cos(\theta) = \frac{\text{adjacent}}{\text{hypotenuse}} \] Rearranging for the adjacent side, we have: \[ \text{adjacent} = \text{hypotenuse} \times \cos(\theta) \]

Substitute the given values into the equation: \[ \text{adjacent} = 25 \times \cos(30^\circ) \] Convert the angle from degrees to radians: \[ 30^\circ = 0.5236 \text{ radians} \] Calculate the cosine: \[ \cos(0.5236) \approx 0.8660 \] Thus, the distance from the wall is: \[ \text{adjacent} = 25 \times 0.8660 \approx 21.65 \text{ feet} \]

Final Answer