A building casts a shadow of 12 meters when the angle of elevation of the sun is

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Question: A building casts a shadow of 12 meters when the angle of elevation of the sun is 30 degrees. What is the height of the building?

Options:

Correct Answer: 18 meters

Solution:

Using tan(30) = height/shadow length, height = shadow length * tan(30) = 12 * √3 = 12√3 meters.

A building casts a shadow of 12 meters when the angle of elevation of the sun is 30 degrees. What is the height of the building?

A building casts a shadow of 12 meters when the angle of elevation of the sun is 30 degrees. What is the height of the building?

Step 1: Understand that the shadow of the building and the height of the building form a right triangle with the ground.
Step 2: Identify the angle of elevation of the sun, which is given as 30 degrees.
Step 3: Recall the trigonometric function tangent (tan), which relates the angle to the opposite side (height of the building) and the adjacent side (length of the shadow).
Step 4: Write the formula for tangent: tan(angle) = opposite/adjacent. Here, tan(30) = height/shadow length.
Step 5: Substitute the known values into the formula: tan(30) = height/12.
Step 6: Calculate tan(30). The value of tan(30 degrees is √3/3.
Step 7: Set up the equation: √3/3 = height/12.
Step 8: Solve for height by multiplying both sides by 12: height = 12 * (√3/3).
Step 9: Simplify the equation: height = 12√3/3 = 4√3 meters.

Trigonometry – The problem involves using the tangent function to relate the angle of elevation to the height of the building and the length of its 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.