From the top of a 50-meter high building, the angle of depression to a point on the ground is 30 degrees. How far is the point from the base of the building?

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25√3 meters
50 meters
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100 meters

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Q: From the top of a 50-meter high building, the angle of depression to a point on the ground is 30 degrees. How far is the point from the base of the building?

Solution: Distance = height / tan(angle) = 50 / (1/√3) = 50√3 meters.

Steps: 11

Step 1: Understand the problem. We have a building that is 50 meters tall.
Step 2: The angle of depression from the top of the building to a point on the ground is 30 degrees.
Step 3: Visualize the situation. Draw a right triangle where the height of the building is one side (50 meters), the distance from the base of the building to the point on the ground is the other side, and the line of sight from the top of the building to the point on the ground is the hypotenuse.
Step 4: Use the tangent function. In a right triangle, the tangent of an angle is the opposite side (height of the building) divided by the adjacent side (distance from the base).
Step 5: Write the formula: tan(angle) = opposite / adjacent. Here, tan(30 degrees) = height / distance.
Step 6: We know the height is 50 meters and tan(30 degrees) is 1/√3.
Step 7: Set up the equation: 1/√3 = 50 / distance.
Step 8: Rearrange the equation to find distance: distance = height / tan(30 degrees).
Step 9: Substitute the values: distance = 50 / (1/√3).
Step 10: Simplify the equation: distance = 50 * √3.
Step 11: Calculate the final answer: distance = 50√3 meters.

From the top of a 50-meter high building, the angle of depression to a point on the ground is 30 degrees. How far is the point from the base of the building?

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