If a 12-meter tall pole casts a shadow of 8 meters, what is the angle of elevati

If a 12-meter tall pole casts a shadow of 8 meters, what is the angle of elevation of the sun?

If a 12-meter tall pole casts a shadow of 8 meters, what is the angle of elevation of the sun?

Correct Answer: 56.31 degrees

Step 1: Understand that the height of the pole is 12 meters and the length of the shadow is 8 meters.
Step 2: Recognize that the angle of elevation (θ) can be found using the tangent function, which relates the height of the pole to the length of the shadow.
Step 3: Write the formula for tangent: tan(θ) = height of the pole / length of the shadow.
Step 4: Substitute the values into the formula: tan(θ) = 12 / 8.
Step 5: Simplify the fraction: 12 / 8 = 1.5.
Step 6: Now, use the inverse tangent function to find the angle: θ = tan^(-1)(1.5).
Step 7: Calculate the angle using a calculator: θ ≈ 56.31 degrees.

Trigonometry – The problem involves using the tangent function to relate the height of the pole and the length of the shadow to find the angle of elevation.
Angle of Elevation – Understanding the concept of angle of elevation, which is the angle formed by the line of sight from the observer to the top of the object.