A person standing 30 meters away from a building observes the top of the buildin

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What’s inside this PDF?

Question: A person standing 30 meters 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?

Options:

15√3 meters
30 meters
20 meters
10√3 meters

Correct Answer: 15√3 meters

Solution:

Using tan(60°) = height / distance, we have height = distance * tan(60°) = 30 * √3 = 15√3 meters.

A person standing 30 meters away from a building observes the top of the buildin

Practice Questions

A person standing 30 meters 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?

15√3 meters
30 meters
20 meters
10√3 meters

Questions & Step-by-Step Solutions

A person standing 30 meters 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?

Step 1: Understand the problem. A person is standing 30 meters away from a building and sees the top of the building at an angle of 60 degrees.
Step 2: Identify the right triangle formed by the person, the top of the building, and the base of the building.
Step 3: Recognize that the distance from the person to the building is the base of the triangle, which is 30 meters.
Step 4: The angle of elevation to the top of the building is 60 degrees.
Step 5: Use the tangent function, which relates the angle to the opposite side (height of the building) and the adjacent side (distance from the building).
Step 6: Write the formula: tan(60°) = height / distance.
Step 7: Substitute the known values into the formula: tan(60°) = height / 30.
Step 8: Calculate tan(60°), which is √3.
Step 9: Rewrite the equation: √3 = height / 30.
Step 10: Solve for height by multiplying both sides by 30: height = 30 * √3.
Step 11: Calculate the height: height = 30 * √3 = 15√3 meters.

Trigonometry – The problem involves using the tangent function to relate the angle of elevation to the height of the building and the distance from it.
Angle of Elevation – Understanding how to interpret the angle of elevation from a horizontal line to the top of an object.
Right Triangle Properties – The scenario can be visualized as a right triangle where the height of the building is the opposite side, the distance from the building is the adjacent side, and the angle of elevation is the angle between them.

A person standing 30 meters away from a building observes the top of the buildin

What’s inside this PDF?

A person standing 30 meters away from a building observes the top of the buildin

Practice Questions

Questions & Step-by-Step Solutions

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