From a point on the ground, the angle of elevation to the top of a 75 m high building is 45 degrees. How far is the point from the building?
Practice Questions
1 question
Q1
From a point on the ground, the angle of elevation to the top of a 75 m high building is 45 degrees. How far is the point from the building?
75 m
50 m
100 m
25 m
Using tan(45°) = height/distance, we have distance = height/tan(45°) = 75/1 = 75 m.
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 75 m high building is 45 degrees. How far is the point from the building?
Solution: Using tan(45°) = height/distance, we have distance = height/tan(45°) = 75/1 = 75 m.
Steps: 8
Step 1: Understand that the angle of elevation is the angle formed between the horizontal ground and the line of sight to the top of the building.
Step 2: Identify the height of the building, which is given as 75 meters.
Step 3: Recognize that the angle of elevation to the top of the building is 45 degrees.
Step 4: Use the tangent function, which relates the angle of elevation to the height of the building and the distance from the building. The formula is: tan(angle) = height/distance.
Step 5: Substitute the known values into the formula: tan(45°) = height/distance, which becomes tan(45°) = 75/distance.
Step 6: Know that tan(45°) equals 1. So, the equation simplifies to: 1 = 75/distance.
Step 7: Rearrange the equation to find the distance: distance = 75/1.
Step 8: Calculate the distance, which equals 75 meters.
