A building is 40 m tall. From a point on the ground, the angle of elevation to the top of the building is 45 degrees. How far is the point from the base of the building? (2020)
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A building is 40 m tall. From a point on the ground, the angle of elevation to the top of the building is 45 degrees. How far is the point from the base of the building? (2020)
Q: A building is 40 m tall. From a point on the ground, the angle of elevation to the top of the building is 45 degrees. How far is the point from the base of the building? (2020)
Step 1: Understand the problem. We have a building that is 40 meters tall.
Step 2: Identify the angle of elevation from the ground to the top of the building, which is 45 degrees.
Step 3: Recall the relationship between the height of the building, the distance from the point to the base of the building, and the angle of elevation. We can use the tangent function.
Step 4: Write down the formula for distance: Distance = height / tan(angle).
Step 5: Substitute the values into the formula: Distance = 40 m / tan(45 degrees).
Step 6: Calculate tan(45 degrees), which is equal to 1.
Step 7: Now, substitute tan(45) into the formula: Distance = 40 m / 1.
Step 8: Perform the division: Distance = 40 m.
Step 9: Conclude that the point is 40 meters away from the base of the building.
