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 to the nearest 0.1 foot.
a. 19 ft
b. 18.6 ft
c. 18.7 ft
d. 18.8 ft

Explanation:

Step1: Use the cosine function

The ladder is the hypotenuse (\(c = 25\) ft) of a right - triangle. Let the height of the house be \(a\). The angle between the ladder and the wall is \(\theta=41.5^{\circ}\). The cosine function is \(\cos\theta=\frac{a}{c}\).
So, \(a = c\times\cos\theta\).

Step2: Substitute the values

Substitute \(c = 25\) and \(\theta = 41.5^{\circ}\) into the formula.
\(a=25\times\cos(41.5^{\circ})\).
We know that \(\cos(41.5^{\circ})\approx0.749\).
Then \(a = 25\times0.749=18.725\approx18.7\) ft.

Answer:

C. \(18.7\) ft