A building is 80 meters tall. From a point on the ground, the angle of elevation to the top of the building is 60 degrees. How far is the point from the base of the building?
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A building is 80 meters tall. From a point on the ground, the angle of elevation to the top of the building is 60 degrees. How far is the point from the base of the building?
Q: A building is 80 meters tall. From a point on the ground, the angle of elevation to the top of the building is 60 degrees. How far is the point from the base of the building?
Step 1: Understand the problem. We have a building that is 80 meters tall and we want to find out how far away a point on the ground is from the base of the building.
Step 2: Identify the angle of elevation. The angle of elevation to the top of the building is given as 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 base).
Step 4: Set up the equation. We can write the equation as tan(60 degrees) = height / distance.
Step 5: Substitute the known values. We know the height is 80 meters, so we have tan(60 degrees) = 80 / distance.
Step 6: Find the value of tan(60 degrees). The value of tan(60 degrees) is √3.
Step 7: Rewrite the equation. Now we have √3 = 80 / distance.
Step 8: Rearrange the equation to solve for distance. Multiply both sides by distance: distance * √3 = 80.
Step 9: Divide both sides by √3 to isolate distance. So, distance = 80 / √3.
Step 10: Simplify the answer. We can also express this as distance = 80√3 / 3 meters.
