QuestionTo estimate the height of a building, two students find the angle of elevation from a point (at ground level) down the street from the building to the top of the building is .
From a point that is 200 feet closer to the building, the angle of elevation (at ground level) to the top of the building is . If we assume that the street is level, use this information to estimate the height of the building. Give your answer to the nearest foot. Put units in the second box.
The height of the building is
Studdy Solution
STEP 1
1. The street is level.
2. The angles of elevation are measured from ground level.
3. The distance between the two points is feet.
STEP 2
1. Set up the trigonometric equations using the tangent function.
2. Solve for the height of the building using the two equations.
3. Calculate the height of the building.
STEP 3
Set up the trigonometric equations using the tangent function. Let be the height of the building and be the distance from the first point to the base of the building.
From the first point:
From the second point, which is 200 feet closer:
STEP 4
Solve for the height of the building using the two equations. First, express in terms of from both equations:
From the first equation:
From the second equation:
Set the two expressions for equal to each other:
STEP_2.1:
Solve the equation for :
Rearrange terms:
Solve for :
STEP 5
Calculate the height of the building. Substitute back into the equation for :
Substitute the value of from STEP_2.1:
Calculate the numerical value:
1. Calculate and .
2. Substitute these values into the equation for .
3. Use the value of to find .
After calculations, the height is approximately:
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