Question

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?

Answer 1

[AI-generated answer — Bot GPT 3.5]

To measure the height of the house, we can use trigonometry. Let's label the height of the house as 'h'.

Using the angle of elevation of 58 degrees, we can create a right triangle with the height of the house as the opposite side and the distance from the base of the house to the sidewalk as the adjacent side.

Using the tangent function, which is defined as the ratio of the opposite side to the adjacent side in a right triangle, we can set up the following equation:

tan(58°) = h/25

Now, let's solve for 'h':

h = tan(58°) * 25

Using a scientific calculator or trigonometric table, we find that tan(58°) is approximately 1.5804.

h ≈ 1.5804 * 25
h ≈ 39.51

Therefore, the height of the house is approximately 39.51 feet when rounded to the nearest foot.