A person standing 50 m away from a building observes the top of the building at an angle of elevation of 60 degrees. What is the height of the building?
Practice Questions
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Q1
A person standing 50 m away from a building observes the top of the building at an angle of elevation of 60 degrees. What is the height of the building?
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Using tan(60°) = height/50, we have √3 = height/50. Therefore, height = 50√3 ≈ 86.6 m.
Questions & Step-by-step Solutions
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Q
Q: A person standing 50 m away from a building observes the top of the building at an angle of elevation of 60 degrees. What is the height of the building?
Solution: Using tan(60°) = height/50, we have √3 = height/50. Therefore, height = 50√3 ≈ 86.6 m.
Steps: 7
Step 1: Understand the problem. A person is standing 50 meters away from a building and sees the top of the building at an angle of 60 degrees.
Step 2: Visualize the situation. Imagine a right triangle where one side is the height of the building, the other side is the distance from the person to the building (50 m), and the angle at the person's position is 60 degrees.
Step 3: Recall the tangent function. In a right triangle, the tangent of an angle is the opposite side (height of the building) divided by the adjacent side (distance to the building).
Step 4: Write the equation using the tangent function. For 60 degrees, we have tan(60°) = height / 50.
Step 5: Substitute the value of tan(60°). We know that tan(60°) = √3, so the equation becomes √3 = height / 50.
Step 6: Solve for the height. Multiply both sides by 50 to isolate height: height = 50 * √3.
Step 7: Calculate the height. Using the approximate value of √3 (about 1.732), we find height ≈ 50 * 1.732 ≈ 86.6 meters.
