To measure the height of your house using the angle of elevation, we can use trigonometry.
Let's assume H is the height of your house (in feet).
We have a right triangle where:
1. The side opposite the angle of elevation (58 degrees) is the height of your house (H).
2. The side adjacent to the angle of elevation is the distance from the sidewalk to the base of your house, which is 25 feet.
3. The hypotenuse is the line of sight from the sidewalk to the top of your house.
Using the trigonometric function tangent (tan), we can set up the equation:
tan(58 degrees) = H / 25
To find H, we'll solve for it:
H = tan(58 degrees) * 25
Calculating this using a calculator or trigonometric table, we find:
H ≈ 36.5 feet
Therefore, your house is approximately 36.5 feet tall (to the nearest foot).
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 steps only
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