the angle of elevations from the top of the tree to the point on the ground is 63 yards from its base 45degrees. How tall is the tree?

h/63 = sin 45

To find the height of the tree, we can use trigonometry and the angle of elevation. Let's break down the problem step by step:

1. Draw a diagram: Draw a vertical line to represent the tree. Mark a point on the ground that is 63 yards away from the base of the tree. Create a right triangle by drawing a line from the top of the tree to the point on the ground.

2. Identify the given information: From the problem, we know that the distance from the top of the tree to the point on the ground is 63 yards, and the angle of elevation, measured from the base of the tree, is 45 degrees.

3. Determine which trigonometric function to use: Since we have the opposite side length (the height of the tree) and the adjacent side length (the distance from the base to the point on the ground), we can use the tangent function.

4. Apply the tangent function: The tangent of an angle is equal to the ratio of the opposite side to the adjacent side. In this case, we have:

tan(angle) = opposite / adjacent

tan(45 degrees) = opposite / 63 yards

5. Solve for the height of the tree: Rearrange the equation to solve for the opposite side, which represents the height of the tree:

opposite = tan(45 degrees) * 63 yards

Using a calculator, find the tangent of 45 degrees: tan(45) ≈ 1

Therefore, the height of the tree is:

opposite = 1 * 63 yards

opposite = 63 yards

So, the tree is approximately 63 yards tall.