Question

question 8 of 10
a 10 - foot ladder is leaning against a building. the ladder makes a 45 - degree angle with the building. how far up the building does the ladder reach?
a. 5\sqrt{2} feet
b. 10\sqrt{2} feet
c. 20\sqrt{2} feet
d. 5 feet

Explanation:

Step1: Identify right triangle components

Hypotenuse (ladder) = 10 ft, angle with building = 45°, height (h) = adjacent side.

Step2: Apply cosine function

$\cos(45^\circ) = \frac{h}{10}$

Step3: Solve for h

$h = 10 \cdot \cos(45^\circ) = 10 \cdot \frac{\sqrt{2}}{2} = 5\sqrt{2}$

Answer:

A. 5√2 feet