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. How tall is the building?

Options:

15√3 meters
30 meters
20 meters
25 meters

Correct Answer: 15√3 meters

Solution:

Using tan(60°) = height/30, height = 30 * √3 = 30√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. How tall is the building?

15√3 meters
30 meters
20 meters
25 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. How tall is the building?

Step 1: Understand the problem. You have a person standing 30 meters away from a building and looking up at 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 (30 meters), and the angle between the ground and the line of sight to the top of the building is 60 degrees.
Step 3: Use 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 from the person to the building). So, tan(60°) = height / 30.
Step 4: Find the value of tan(60°). The value of tan(60°) is √3.
Step 5: Set up the equation. Replace tan(60°) in the equation: √3 = height / 30.
Step 6: Solve for height. Multiply both sides of the equation by 30: height = 30 * √3.
Step 7: Calculate the height. The height of the building is 30√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 the building.
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 given.

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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