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
To solve this problem, we can use the trigonometric function tangent.
We know that the tangent of an angle is equal to the ratio of the opposite side to the adjacent side. In this case, the opposite side is the height of the house and the adjacent side is the distance from the base of the house to the sidewalk.
Let h be the height of the house.
Using the tangent function:
tan(58 degrees) = h / 25 [tan(θ) = opposite/adjacent]
To find h, we can rearrange the equation:
h = tan(58 degrees) * 25
Using a calculator, we can calculate the value of h:
h ≈ 1.738 * 25
h ≈ 43.45 feet
Therefore, the height of your house is approximately 43.45 feet to the nearest foot.