Question

A twenty-five foot ladder just reaches the top of a house and forms an angle of 41.5° with the wall of the house. how tall is the house? round your answer to the nearest 0.1 foot.

Answer 1

Answer:

The wall is approximately 10.75 feet tall.

Step-by-step explanation:

This problem is about a right triangle formed by the ladder and the house. The given triangle is formed with the wall, that is, is the space between the wall and the ladder. The twenty-five foot refers to the hypothenuse of the right triangle formed, and the wall is the vertical leg.

Therefore, we have to use trigonometric reasons to answer the questions, because we know an angle and the hypothenuses of the triangle. The relations we must use is:

$cos(\alpha )=\frac{x}{h}$

Replacing given values, we have:

$cos(41.5)=\frac{x}{25}$

$x=25cos(41.5)=25(0.75) \approx 18.75 \ ft$

Therefore, the wall is approximately 10.75 feet tall.

Answer 2

So to find this we must use cos(41.5 degrees) so the equation is cos(41.5)=x/25 we times both sides by 25. We also find out what cos 41.5 is in this step. so 0.75x25 = x. Therefore x=18.8. the house is 18.8 feet tall