A man is standing on the ground and looking at the top of a 40 m high building.

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What’s inside this PDF?

Question: A man is standing on the ground and looking at the top of a 40 m high building. If the angle of elevation is 60 degrees, how far is he from the building?

Options:

20 m
40 m
20√3 m
40√3 m

Correct Answer: 20√3 m

Solution:

Using tan(60°) = height/distance, we have distance = height/tan(60°) = 40/√3 = 20√3 m.

A man is standing on the ground and looking at the top of a 40 m high building.

Practice Questions

A man is standing on the ground and looking at the top of a 40 m high building. If the angle of elevation is 60 degrees, how far is he from the building?

20 m
40 m
20√3 m
40√3 m

Questions & Step-by-Step Solutions

A man is standing on the ground and looking at the top of a 40 m high building. If the angle of elevation is 60 degrees, how far is he from the building?

Step 1: Understand the problem. A man is looking at the top of a 40 m high building from the ground.
Step 2: Identify the angle of elevation. The angle of elevation from the man to the top of the building is 60 degrees.
Step 3: Recall the relationship in a right triangle. 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).
Step 4: Write the formula for tangent. tan(60°) = height / distance.
Step 5: Substitute the known values into the formula. tan(60°) = 40 m / distance.
Step 6: Solve for distance. Rearranging gives distance = height / tan(60°).
Step 7: Calculate tan(60°). The value of tan(60°) is √3.
Step 8: Substitute tan(60°) into the equation. distance = 40 m / √3.
Step 9: Simplify the distance. This can be rewritten as distance = 40/√3 m.
Step 10: Rationalize the denominator. Multiply the numerator and denominator by √3 to get distance = (40√3) / 3 m.
Step 11: Final answer. The distance from the man to the building is approximately 20√3 m.

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 – Understanding the relationship between the sides of a right triangle formed by the height of the building, the distance from the building, and the line of sight.

A man is standing on the ground and looking at the top of a 40 m high building.

What’s inside this PDF?

A man is standing on the ground and looking at the top of a 40 m high building.

Practice Questions

Questions & Step-by-Step Solutions

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