A man is standing on a hill 100 meters high. If he looks down at an angle of 45

A man is standing on a hill 100 meters high. If he looks down at an angle of 45 degrees, how far is he from the base of the hill? (2020)

A man is standing on a hill 100 meters high. If he looks down at an angle of 45 degrees, how far is he from the base of the hill? (2020)

Step 1: Understand that the man is looking down from a height of 100 meters.
Step 2: Recognize that he is looking down at an angle of 45 degrees.
Step 3: Recall that the tangent of an angle in a right triangle is the opposite side (height) divided by the adjacent side (distance from the base).
Step 4: For a 45-degree angle, the tangent value is 1 (tan(45 degrees) = 1).
Step 5: Use the formula: Distance = height / tan(angle).
Step 6: Plug in the values: Distance = 100 meters / 1.
Step 7: Calculate the distance: Distance = 100 meters.

Trigonometry – The question tests the understanding of basic trigonometric functions, specifically the tangent function, which relates the angle of elevation or depression to the opposite and adjacent sides of a right triangle.
Right Triangle Properties – The problem involves a right triangle formed by the height of the hill, the distance from the man to the base of the hill, and the line of sight.