A tower is 60 m high. From a point on the ground, the angle of elevation to the top of the tower is 60 degrees. How far is the point from the base of the tower? (2023)
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A tower is 60 m high. From a point on the ground, the angle of elevation to the top of the tower is 60 degrees. How far is the point from the base of the tower? (2023)
Q: A tower is 60 m high. From a point on the ground, the angle of elevation to the top of the tower is 60 degrees. How far is the point from the base of the tower? (2023)
Step 1: Understand the problem. We have a tower that is 60 meters high and we want to find out how far a point on the ground is from the base of the tower.
Step 2: Identify the angle of elevation. The angle of elevation from the point on the ground to the top of the tower 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 tower) 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: Plug in the values. We know the height is 60 meters, so we have: tan(60) = 60 / distance.
Step 6: Rearrange the equation to find distance. This gives us: distance = height / tan(60).
Step 7: Calculate tan(60 degrees). The value of tan(60 degrees) is √3.
Step 8: Substitute tan(60) into the equation. Now we have: distance = 60 / √3.
Step 9: Simplify the calculation. This can be approximated as distance ≈ 30 meters.
