A fence 2.4 m tall, is 10m away from a tree of height 16m. Calculate the angle of elevation of the top of the tree from the top of the fence.

Answer Details

To solve this problem, we can use trigonometry and the concept of similar triangles. Let's draw a diagram to visualize the situation. We have a fence that is 2.4 meters tall and a tree that is 16 meters tall. The tree is 10 meters away from the fence. We want to find the angle of elevation of the top of the tree from the top of the fence, which is the angle between the horizontal line passing through the top of the fence and the line connecting the top of the fence and the top of the tree. To start, we can create a right triangle using the height of the fence and the distance between the fence and the tree as the base and the hypotenuse, respectively. Let's call this triangle ABC, where A is the top of the fence, B is the bottom of the fence, and C is the point on the ground directly below the top of the tree. The angle between AB and AC is 90 degrees. Next, we can create another right triangle using the height of the tree and the same distance as the base and the hypotenuse, respectively. Let's call this triangle ACD, where D is the top of the tree. The angle between AD and AC is also 90 degrees. Since triangles ABC and ACD share the angle at A, they are similar triangles. This means that their corresponding angles are equal, and their corresponding sides are proportional. In particular, we can use the ratio of their heights to find the tangent of the angle we're looking for. Let's call the angle of elevation we're looking for x. Then, we have: tan(x) = CD/AB = (16-2.4)/10 = 1.36 To solve for x, we take the inverse tangent of both sides: x = tan^-1(1.36) ≈ 53.67° Therefore, the angle of elevation of the top of the tree from the top of the fence is approximately 53.67 degrees.