A tower is 100 meters high. From a point on the ground, the angle of elevation to the top of the tower is 45 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 45 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 45 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 tall.
Step 2: Identify the angle of elevation from the point on the ground to the top of the tower, which is 45 degrees.
Step 3: Recall the relationship between the height of the tower, the distance from the point to the base of the tower, and the angle of elevation. We can use the tangent function.
Step 4: The formula for tangent in a right triangle is: tan(angle) = opposite side / adjacent side.
Step 5: In our case, the opposite side is the height of the tower (100 meters) and the adjacent side is the distance we want to find.
Step 6: Since the angle is 45 degrees, we know that tan(45 degrees) = 1.
Step 7: Set up the equation: tan(45 degrees) = height / distance, which means 1 = 100 / distance.
Step 8: Rearrange the equation to find the distance: distance = height / tan(45 degrees).
Step 9: Substitute the values: distance = 100 / 1.
Step 10: Calculate the distance: distance = 100 meters.
