A 10-meter tall pole casts a shadow of 5 meters long. What is the angle of eleva

A 10-meter tall pole casts a shadow of 5 meters long. What is the angle of elevation of the sun?

A 10-meter tall pole casts a shadow of 5 meters long. What is the angle of elevation of the sun?

Correct Answer: 60 degrees

Step 1: Identify the height of the pole, which is 10 meters.
Step 2: Identify the length of the shadow, which is 5 meters.
Step 3: Use the tangent function, which relates the angle of elevation to the height and shadow length. The formula is tan(angle) = height / shadow.
Step 4: Substitute the values into the formula: tan(angle) = 10 / 5.
Step 5: Calculate the right side: 10 divided by 5 equals 2, so tan(angle) = 2.
Step 6: To find the angle, use the inverse tangent function (also called arctan) on the value 2: angle = arctan(2).
Step 7: Use a calculator or a trigonometric table to find the angle. The angle is approximately 60 degrees.

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