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 elevation to the top your house is 48° how tall is your house to the nearest foot
To determine the height of your house based on the given information, we can use trigonometry.
Let's consider the height of your house as 'h'. We know that the distance from the base of your house to the sidewalk is 25 feet, and the angle of elevation from the sidewalk to the top of your house is 48°.
In a right triangle, the tangent of an angle is equal to the ratio of the opposite side to the adjacent side. In this case, the tangent of the angle of elevation (48°) would be given by:
tan(48°) = h/25
To solve for 'h', we rearrange the equation:
h = 25 * tan(48°)
Calculating this expression, we find:
h ≈ 25 * 1.1106 ≈ 27.77 feet
Therefore, your house is approximately 27.77 feet tall to the nearest foot.