From a point on the ground, the angle of elevation to the top of a building is 45 degrees. If the point is 20 meters away from the building, what is the height of the building?
Practice Questions
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Q1
From a point on the ground, the angle of elevation to the top of a building is 45 degrees. If the point is 20 meters away from the building, what is the height of the building?
20 meters
10 meters
30 meters
25 meters
Height = distance * tan(45) = 20 * 1 = 20 meters.
Questions & Step-by-step Solutions
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Q
Q: From a point on the ground, the angle of elevation to the top of a building is 45 degrees. If the point is 20 meters away from the building, what is the height of the building?
Step 1: Understand that the angle of elevation is the angle formed between the horizontal line from your point on the ground and the line of sight to the top of the building.
Step 2: Recognize that when the angle of elevation is 45 degrees, the height of the building is equal to the distance from the point to the building.
Step 3: Note that the distance from the point on the ground to the building is given as 20 meters.
Step 4: Use the tangent function, which relates the angle of elevation to the height and distance. For 45 degrees, tan(45) equals 1.
Step 5: Calculate the height of the building using the formula: Height = distance * tan(angle). Here, Height = 20 meters * tan(45 degrees).
Step 6: Since tan(45 degrees) is 1, the calculation simplifies to Height = 20 meters * 1.
Step 7: Conclude that the height of the building is 20 meters.
