If the sun's angle of elevation is 30°, what is the height of a building that ca

₹0.0

Question: If the sun\'s angle of elevation is 30°, what is the height of a building that casts a shadow of 10 m? (2022)

Options:

Correct Answer: 5 m

Exam Year: 2022

Solution:

Height = Shadow length * tan(angle) = 10 m * tan(30°) = 10 m * (1/√3) ≈ 5 m.

If the sun's angle of elevation is 30°, what is the height of a building that casts a shadow of 10 m? (2022)

If the sun's angle of elevation is 30°, what is the height of a building that casts a shadow of 10 m? (2022)

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: Identify the length of the shadow, which is given as 10 meters.
Step 3: Recognize that we need to use the tangent function to find the height of the building. The formula is: Height = Shadow length * tan(angle).
Step 4: Substitute the values into the formula. Here, the angle is 30° and the shadow length is 10 m: Height = 10 m * tan(30°).
Step 5: Calculate tan(30°). The value of tan(30°) is 1/√3.
Step 6: Multiply the shadow length by the tangent value: Height = 10 m * (1/√3).
Step 7: Calculate the height: Height ≈ 10 m * 0.577 ≈ 5 m.

Trigonometry – The question tests the understanding of the relationship between angles and sides in right triangles, specifically using the tangent function.
Angle of Elevation – The concept of angle of elevation is crucial for determining the height of an object based on the length of its shadow.