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. 24\sqrt{2} feet
b. 6 feet
c. 6\sqrt{2} feet
d. 12\sqrt{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 side adjacent to the 45 - degree angle ($a$). We use the cosine function: $\cos\theta=\frac{a}{c}$.

Step2: Substitute the values

Since $\theta = 45^{\circ}$ and $c = 12$, and $\cos45^{\circ}=\frac{\sqrt{2}}{2}$, we have $\frac{\sqrt{2}}{2}=\frac{a}{12}$.

Step3: Solve for $a$

Cross - multiply to get $a = 12\times\frac{\sqrt{2}}{2}=6\sqrt{2}$ feet.

Answer:

C. $6\sqrt{2}$ feet