From the top of a 40-meter high tower, the angle of depression to a point on the ground is 45 degrees. How far is the point from the base of the tower?
Practice Questions
1 question
Q1
From the top of a 40-meter high tower, the angle of depression to a point on the ground is 45 degrees. How far is the point from the base of the tower?
40 meters
30 meters
50 meters
20 meters
distance = height / tan(45) = 40 / 1 = 40 meters
Questions & Step-by-step Solutions
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Q
Q: From the top of a 40-meter high tower, the angle of depression to a point on the ground is 45 degrees. How far is the point from the base of the tower?
Step 1: Understand that the tower is 40 meters high.
Step 2: Recognize that the angle of depression is the angle formed from the top of the tower down to the point on the ground.
Step 3: Note that an angle of depression of 45 degrees means that the angle from the horizontal line down to the point is 45 degrees.
Step 4: Use the tangent function, which relates the height of the tower to the distance from the base of the tower. The formula is: tan(angle) = opposite/adjacent.
Step 5: In this case, the opposite side is the height of the tower (40 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) = height / distance, which simplifies to 1 = 40 / distance.
Step 8: Rearrange the equation to find the distance: distance = height / tan(45).
Step 9: Substitute the height into the equation: distance = 40 / 1.
Step 10: Calculate the distance: distance = 40 meters.
