If the angle of elevation of the sun is 30 degrees, how tall is a 10 meter pole
Practice Questions
Q1
If the angle of elevation of the sun is 30 degrees, how tall is a 10 meter pole casting a shadow?
5√3 m
10 m
10√3 m
5 m
Questions & Step-by-Step Solutions
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.
