A building casts a shadow of 20 meters when the angle of elevation of the sun is 45 degrees. What is the height of the building?

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Q: A building casts a shadow of 20 meters when the angle of elevation of the sun is 45 degrees. What is the height of the building?

Solution: Height = shadow * tan(45) = 20 * 1 = 20 meters

Steps: 7

Step 1: Understand that the angle of elevation is the angle between the ground and the line from the top of the building to the sun.
Step 2: Recognize that when the angle of elevation is 45 degrees, the height of the building and the length of the shadow are equal.
Step 3: Use the tangent function, which relates the height of the building to the length of the shadow: tan(angle) = height / shadow.
Step 4: Since the angle is 45 degrees, we know that tan(45) = 1.
Step 5: Set up the equation: height = shadow * tan(45).
Step 6: Substitute the values: height = 20 meters * 1.
Step 7: Calculate the height: height = 20 meters.