Final answer:
Using the sine function and the angle of 62°, the ladder forms with the ground, we calculate the height at which the ladder meets the house to be approximately 22.36 ft, making the closest answer 21.5 ft.
Step-by-step explanation:
To determine how high above the ground the base of the roof is, given that a 25 ft. ladder is leaning against the house with an angle of 62° with the ground, we can use trigonometry. Specifically, we will use the sine function since we are looking for the opposite side of the right triangle formed by the ladder, the wall of the house, and the ground. The sine of an angle in a right triangle is equal to the length of the side opposite the angle divided by the hypotenuse. Therefore, sin(62°) = height / 25 ft. Solving for the height gives us height = 25 ft × sin(62°). After performing the calculation, we find that the height is approximately 22.36 ft, which means the closest answer to the provided options is A. 21.5 ft.