A tower is 100 meters high. From a point on the ground, the angle of elevation to the top of the tower is 30 degrees. How far is the point from the base of the tower?
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A tower is 100 meters high. From a point on the ground, the angle of elevation to the top of the tower is 30 degrees. How far is the point from the base of the tower?
Q: A tower is 100 meters high. From a point on the ground, the angle of elevation to the top of the tower is 30 degrees. How far is the point from the base of the tower?
Step 1: Understand the problem. We have a tower that is 100 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 to the top of the tower is given as 30 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: Substitute the values into the formula. Here, height = 100 meters and angle = 30 degrees. So, Distance = 100 / tan(30 degrees).
Step 6: Calculate tan(30 degrees). The value of tan(30 degrees) is 1/√3.
Step 7: Substitute tan(30 degrees) into the formula. Now we have Distance = 100 / (1/√3).
Step 8: Simplify the equation. Dividing by a fraction is the same as multiplying by its reciprocal, so Distance = 100 * √3.
Step 9: Final calculation. Therefore, the distance from the point to the base of the tower is 100√3 meters.
