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.
Let's denote the height of the house as 'h'.
Using trigonometry, we can set up the tangent function as follows:
tan(58 degrees) = h / 25 feet
To find 'h', we can rearrange the equation:
h = 25 feet * tan(58 degrees)
Using a calculator to find the tangent of 58 degrees:
h ≈ 25 feet * 1.61
Therefore, the height of your house is approximately 40.25 feet (rounded to the nearest foot).