A tower is 50 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 50 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 50 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 that the tower is 50 meters high.
Step 2: Know that the angle of elevation to the top of the tower is 45 degrees.
Step 3: Recall that the tangent of an angle in a right triangle is the opposite side (height of the tower) divided by the adjacent side (distance from the base).
Step 4: Use the formula: Distance = height / tan(angle).
Step 5: Since tan(45 degrees) = 1, substitute the values: Distance = 50 meters / 1.
Step 6: Calculate the distance, which equals 50 meters.
