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The angle of elevation to the top of a very tall Building is found to be 7° from the ground at a distance of 1 mi from the base of the building. Using this information, find the height of the building.
Draw yourself a picture
Let building height = y
Distance from observer to base = x
= 1 mile = 5280 feet
y/x = tan(7deg) = 0.12278
y = 648.3 feet
To find the height of the building, we can use trigonometry. Let's break down the information we have:
Angle of elevation: 7°
Distance from the base of the building: 1 mile
To solve this problem, we'll use the tangent function. The tangent of an angle is defined as the ratio of the length of the opposite side to the length of the adjacent side.
In this case, the opposite side will be the height of the building, and the adjacent side will be the distance from the base of the building.
Let's define our variables:
h = height of the building
d = distance from the base of the building
Using the tangent function, we can set up the following equation:
tan(7°) = h/d
Now we need to rearrange the equation to solve for h:
h = d * tan(7°)
Given that the distance from the base of the building is 1 mile (d = 1), the equation becomes:
h = 1 * tan(7°)
To calculate the height, we need to evaluate tan(7°). Here's how you can do it:
1. Convert the angle from degrees to radians. Since most scientific calculators work with radians, we need to convert 7° to radians. To convert degrees to radians, use the following formula:
radians = degrees * (π/180)
In our case, the formula becomes:
radians = 7° * (π/180) ≈ 0.122 radians
2. Once you have the angle in radians, you can calculate the tangent. Use the tangent function (tan) on your calculator:
tan(0.122) ≈ 0.1229
Now we can substitute the value of tan(7°) back into the equation:
h = 1 * 0.1229
After evaluating the expression, we find that the height of the building is approximately 0.1229 miles.