A building casts a shadow of 20 meters when the angle of elevation of the sun is

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

Options:

Correct Answer: 20 meters

Solution:

Using tan(45°) = height/20, height = 20 * 1 = 20 meters.

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

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

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°, the height of the building and the length of the shadow are equal.
Step 3: Note that the shadow of the building is 20 meters long.
Step 4: Use the tangent function, which relates the angle of elevation to the height of the building and the length of the shadow: tan(angle) = height / shadow length.
Step 5: Substitute the values into the equation: tan(45°) = height / 20.
Step 6: Since tan(45°) equals 1, the equation simplifies to 1 = height / 20.
Step 7: Multiply both sides by 20 to find the height: height = 20 * 1.
Step 8: Conclude that the height of the building is 20 meters.

Trigonometry – The problem involves using the tangent function to relate the angle of elevation of the sun to the height of the building and the length of the shadow.
Angle of Elevation – Understanding how the angle of elevation affects the relationship between the height of an object and the length of its shadow.