A person is standing 50 m away from a building. If the angle of elevation to the top of the building is 30 degrees, what is the height of the building?
Practice Questions
1 question
Q1
A person is standing 50 m away from a building. If the angle of elevation to the top of the building is 30 degrees, what is the height of the building?
25√3 m
50 m
30 m
40 m
Using tan(30°) = height/50, we have 1/√3 = height/50. Therefore, height = 50/√3 m.
Questions & Step-by-step Solutions
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Q
Q: A person is standing 50 m away from a building. If the angle of elevation to the top of the building is 30 degrees, what is the height of the building?
Solution: Using tan(30°) = height/50, we have 1/√3 = height/50. Therefore, height = 50/√3 m.
Steps: 7
Step 1: Understand the problem. A person is standing 50 meters away from a building and looking up at the top of the building at an angle of 30 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 between the ground and the line of sight to the top of the building is 30 degrees.
Step 3: Recall the tangent function. In a right triangle, the tangent of an angle is equal to 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 30 degrees, we have tan(30°) = height / 50.
Step 5: Substitute the value of tan(30°). We know that tan(30°) is equal to 1/√3. So, we can write the equation as 1/√3 = height / 50.
Step 6: Solve for the height. To find the height, multiply both sides of the equation by 50: height = 50 * (1/√3).
Step 7: Simplify the equation. This gives us height = 50/√3 meters.
