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?
To solve this problem, we can use trigonometric functions.
Let's call the height of the house "h".
Since we know the distance from the sidewalk to the base of the house is 25 feet and the angle of elevation is 58 degrees, we can use the tangent function.
The tangent of an angle is the ratio of the length of the opposite side to the length of the adjacent side.
In this case, the opposite side is the height of the house (h), and the adjacent side is the distance from the sidewalk to the base of the house (25 ft).
So, we have: tan(58°) = h / 25 ft.
We can solve for "h" by multiplying both sides of the equation by 25 ft:
25 ft * tan(58°) = h.
Using a calculator, we find that tan(58°) ≈ 1.496, so:
h ≈ 25 ft * 1.496.
h ≈ 37.4 ft.
Therefore, the height of your house is approximately 37.4 feet to the nearest foot.