A person standing 40 m away from a building observes the top of the building at an angle of elevation of 30 degrees. What is the height of the building?
Practice Questions
1 question
Q1
A person standing 40 m away from a building observes the top of the building at an angle of elevation of 30 degrees. What is the height of the building?
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40 m
Using tan(30°) = height/40, we have 1/√3 = height/40. Therefore, height = 40/√3 ≈ 23.1 m.
Questions & Step-by-step Solutions
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Q
Q: A person standing 40 m away from a building observes the top of the building at an angle of elevation of 30 degrees. What is the height of the building?
Solution: Using tan(30°) = height/40, we have 1/√3 = height/40. Therefore, height = 40/√3 ≈ 23.1 m.
Steps: 8
Step 1: Understand the problem. A person is standing 40 meters away from a building and sees the top of the building at an angle of 30 degrees.
Step 2: Visualize the situation. Draw a right triangle where one side is the height of the building, the other side is the distance from the person to the building (40 m), and the angle at the person's position is 30 degrees.
Step 3: Use the tangent function. The tangent of an angle in a right triangle is the opposite side (height of the building) divided by the adjacent side (distance from the building). So, tan(30°) = height / 40.
Step 4: Find the value of tan(30°). We know that tan(30°) = 1/√3.
Step 5: Set up the equation. Replace tan(30°) in the equation: 1/√3 = height / 40.
Step 6: Solve for height. Multiply both sides by 40: height = 40 * (1/√3).
Step 7: Calculate the height. This gives height = 40/√3.
Step 8: Approximate the height. Using a calculator, 40/√3 is approximately 23.1 meters.
