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 your house is 48° how tall is your house to the nearest foot
To find the height of your house, we can use trigonometry. We'll first need to create a right-angled triangle with one side representing the height of the house, another side representing the distance from the sidewalk to the house, and the angle of elevation as the angle between those two sides.
Let's label the height of the house as 'h' and the distance from the sidewalk to the house as '25 feet'. We can then use the trigonometric function tangent (tan) to find the height.
Using the tangent function: tan(angle) = opposite/adjacent
tan(48°) = h/25
To find h, we can rearrange the equation:
h = 25 * tan(48°)
Calculating it:
h ≈ 25 * 1.1106 ≈ 27.77
Therefore, the height of your house is approximately 27.77 feet. Rounding to the nearest foot gives us an estimated height of 28 feet.