If the angle of elevation of the sun is 30 degrees, how tall is a 10 meter pole

₹0.0

Question: If the angle of elevation of the sun is 30 degrees, how tall is a 10 meter pole casting a shadow?

Options:

Correct Answer: 5√3 m

Solution:

Height = shadow * tan(angle) = 10 * √3 = 5√3 m.

If the angle of elevation of the sun is 30 degrees, how tall is a 10 meter pole casting a shadow?

If the angle of elevation of the sun is 30 degrees, how tall is a 10 meter pole casting a shadow?

Step 1: Understand that the angle of elevation is the angle between the ground and the line from the top of the pole to the sun.
Step 2: Identify the height of the pole, which is 10 meters.
Step 3: Recognize that the shadow of the pole and the height of the pole form a right triangle with the angle of elevation.
Step 4: Use the tangent function, which relates the angle of elevation to the height of the pole and the length of the shadow: tan(angle) = height / shadow.
Step 5: Rearrange the formula to find the height: height = shadow * tan(angle).
Step 6: For an angle of 30 degrees, tan(30 degrees) is equal to 1/√3 or √3/3.
Step 7: Substitute the values into the formula: height = shadow * (1/√3).
Step 8: Since the height of the pole is 10 meters, we can find the shadow length: shadow = height / tan(30 degrees) = 10 / (1/√3) = 10 * √3.
Step 9: Calculate the height using the shadow length: height = shadow * tan(30 degrees) = (10 * √3) * (1/√3) = 10 * 1 = 10 meters.

Trigonometry – The problem involves using the tangent function to relate the height of the pole to the length of the shadow based on the angle of elevation.
Angle of Elevation – Understanding how the angle of elevation affects the height of an object casting a shadow.
Shadow Length Calculation – Calculating the length of the shadow using the tangent of the angle of elevation.