A building is 40 m high. From a point on the ground, the angle of elevation to t

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Question: A building is 40 m high. From a point on the ground, the angle of elevation to the top of the building is 60 degrees. What is the distance from the point to the base of the building?

Options:

20√3 m
40 m
30 m
10√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 building is 40 m high. From a point on the ground, the angle of elevation to t

Practice Questions

A building is 40 m high. From a point on the ground, the angle of elevation to the top of the building is 60 degrees. What is the distance from the point to the base of the building?

20√3 m
40 m
30 m
10√3 m

Questions & Step-by-Step Solutions

A building is 40 m high. From a point on the ground, the angle of elevation to the top of the building is 60 degrees. What is the distance from the point to the base of the building?

Correct Answer: 20√3 m

Step 1: Understand the problem. We have a building that is 40 meters high.
Step 2: Identify the angle of elevation from the ground to the top of the building, which is 60 degrees.
Step 3: Recall the relationship in a right triangle: tan(angle) = opposite side / adjacent side.
Step 4: In our case, the opposite side is the height of the building (40 m) and the adjacent side is the distance from the point to the base of the building.
Step 5: Write the equation using the tangent function: tan(60°) = height / distance.
Step 6: Substitute the known values into the equation: tan(60°) = 40 / distance.
Step 7: Rearrange the equation to solve for distance: distance = height / tan(60°).
Step 8: Calculate tan(60°), which is √3.
Step 9: Substitute tan(60°) into the equation: distance = 40 / √3.
Step 10: Simplify the equation: distance = 40 / √3 = 40√3 / 3.
Step 11: To express it in a simpler form, we can multiply the numerator and denominator by √3: distance = 20√3 meters.

Trigonometry – The problem involves using the tangent function to relate the height of the building to the distance from the point on the ground.
Angle of Elevation – Understanding the angle of elevation is crucial for setting up the right triangle in the problem.
Right Triangle Properties – The relationship between the sides of a right triangle and the angles is fundamental to solving the problem.

A building is 40 m high. From a point on the ground, the angle of elevation to t

What’s inside this PDF?

A building is 40 m high. From a point on the ground, the angle of elevation to t

Practice Questions

Questions & Step-by-Step Solutions

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