To solve this problem, we can use trigonometry. Let's label the height of the house as "h".
Using the given information, we have a right triangle formed by the sidewalk, the base of the house, and the top of the house. The angle of elevation to the top of the house is 58 degrees, which means the angle between the sidewalk and the line from the base of the house to the top of the house is 90 - 58 = 32 degrees.
Using trigonometry, we can use the tangent function to find the height of the house.
tan(32 degrees) = h / 25 feet
To solve for h, we can multiply both sides by 25 feet:
25 feet * tan(32 degrees) = h
Using a calculator, we find:
h ≈ 14.99 feet
Therefore, the height of your house is approximately 15 feet to the nearest foot.
You are trying to measure the height of your house but only have a surveyor tool that measures angles and you know your sidewalk is exactly 25 feet from the base of your home. From the sidewalk, you find that the measure of the angle of elevation to the top of your house is 58 degrees. How tall is your house to the nearest foot? Please show all work in order to get full credit. (2 points)
1 answer