If a person is 20 meters away from a tree and the angle of elevation to the top

If a person is 20 meters away from a tree and the angle of elevation to the top of the tree is 45 degrees, what is the height of the tree?

If a person is 20 meters away from a tree and the angle of elevation to the top of the tree is 45 degrees, what is the height of the tree?

Correct Answer: 20 meters

Step 1: Understand the problem. You have a tree and a person standing 20 meters away from it.
Step 2: The angle of elevation to the top of the tree is given as 45 degrees. This means if you draw a line from the person's eyes to the top of the tree, it makes a 45-degree angle with the ground.
Step 3: In a right triangle, the tangent of an angle is equal to the opposite side (height of the tree) divided by the adjacent side (distance from the tree).
Step 4: The formula for height is: Height = distance * tan(angle).
Step 5: Plug in the values: Height = 20 meters * tan(45 degrees).
Step 6: Since tan(45 degrees) equals 1, the calculation becomes: Height = 20 * 1.
Step 7: Therefore, the height of the tree is 20 meters.

Trigonometry – The problem involves using the tangent function to relate the height of the tree to the distance from the tree and the angle of elevation.
Angle of Elevation – Understanding that the angle of elevation is measured from the horizontal line up to the top of the tree.
Right Triangle Properties – The scenario can be visualized as a right triangle where the height of the tree is the opposite side, the distance from the tree is the adjacent side, and the angle of elevation is the angle between them.