A tower is 40 meters 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?
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A tower is 40 meters 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?
Q: A tower is 40 meters 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?
Step 1: Understand the problem. We have a tower that is 40 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: Write the formula. The formula we will use is: Distance = height / tan(angle).
Step 5: Plug in the values. The height of the tower is 40 meters and the angle is 60 degrees. So, we have: Distance = 40 / tan(60°).
Step 6: Calculate tan(60°). The value of tan(60°) is √3.
Step 7: Substitute tan(60°) into the formula. Now we have: Distance = 40 / √3.
Step 8: Simplify the expression. To make it easier, we can multiply the numerator and denominator by √3: Distance = (40√3) / 3.
Step 9: Final answer. The distance from the point to the base of the tower is approximately 20√3 meters.
