Question

a 12 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. 6√2 feet
b. 6 feet
c. 12√2 feet
d. 24√2 feet

Explanation:

Step1: Identify the right - triangle relationship

We have a right - triangle where the ladder is the hypotenuse ($c = 12$ feet) and we want to find the adjacent side ($x$) to the given angle $\theta=45^{\circ}$ with respect to the building. We use the cosine function $\cos\theta=\frac{x}{c}$.

Step2: Substitute the values

Since $\cos45^{\circ}=\frac{\sqrt{2}}{2}$ and $c = 12$, we have $x = c\cos\theta=12\times\frac{\sqrt{2}}{2}$.

Step3: Simplify the expression

$x = 6\sqrt{2}$ feet.

Answer:

A. $6\sqrt{2}$ feet