Question

A ladder leans against a wall. The bottom of the ladder is 14 feet from the base of the wall and the top of ladder makes a 25 degree angle with the wall. Find the length of the ladder to nearest hundredth.

A. 15.33 feet
B. 15.72 feet
C. 13.45 feet
D. 16.89 feet

Answer 1

The length of the ladder that leans against the wall at a 25-degree angle and is 14 feet away from the base of the wall is calculated using the cosine function, yielding an approximate length of 15.72 feet.

Step-by-step explanation:

To find the length of the ladder, we can use trigonometry, specifically the cosine function, which relates the angle, adjacent side, and hypotenuse in a right triangle. In this case, the wall forms the right angle with the ground, making the ladder the hypotenuse, the ground the adjacent side, and the 25-degree angle is given. We can use the cosine function as follows:

cos(25°) = adjacent/hypotenuse

cos(25°) = 14 feet / Length of ladder

Length of ladder = 14 feet / cos(25°)

After calculating, the length of the ladder to the nearest hundredth is approximately 15.72 feet, which corresponds to option B.