From a point on the ground, the angle of elevation to the top of a 40 m high building is 45 degrees. How far is the point from the base of the building?
Practice Questions
1 question
Q1
From a point on the ground, the angle of elevation to the top of a 40 m high building is 45 degrees. How far is the point from the base of the building?
40 m
20 m
30 m
50 m
Using tan(45°) = height/distance, we have distance = height/tan(45°) = 40/1 = 40 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 40 m high building is 45 degrees. How far is the point from the base of the building?
Solution: Using tan(45°) = height/distance, we have distance = height/tan(45°) = 40/1 = 40 m.
Steps: 10
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 40 meters.
Step 3: Recognize that the angle of elevation 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.
Step 5: Write the formula: tan(angle) = height/distance.
Step 6: Substitute the known values into the formula: tan(45°) = height (40 m) / distance.
Step 7: Know that tan(45°) equals 1, so the equation becomes 1 = 40 m / distance.
Step 8: Rearrange the equation to find distance: distance = height / tan(45°).
Step 9: Substitute the values: distance = 40 m / 1.
