At a point on the ground 50 feet from the front of a tree, the angle of elevation to the top of the tree is 48 degrees. Find the height of the tree.

To solve this problem, we can use trigonometry. Assuming the ground is level, we can create a right triangle with the tree height as the opposite side, the distance from the tree as the adjacent side, and the angle of elevation as the angle.

1. Given information:
- Distance from the front of the tree to the point on the ground = 50 feet
- Angle of elevation = 48 degrees

2. Identify the sides of the triangle:
- Opposite side: height of the tree
- Adjacent side: 50 feet (distance from the front of the tree to the point on the ground)

3. Recall the trigonometric function tangent (tan):
- tan(angle) = opposite side / adjacent side

4. Substitute the known values into the formula:
- tan(48 degrees) = tree height / 50 feet

5. Solve for the tree height:
- tree height = tan(48 degrees) * 50 feet

6. Use a calculator to find the tangent of 48 degrees:
- tan(48 degrees) ≈ 1.1106

7. Calculate the tree height:
- tree height ≈ 1.1106 * 50 feet ≈ 55.53 feet (rounded to two decimal places)

Therefore, the height of the tree is approximately 55.53 feet.

To find the height of the tree, we can use trigonometry and the concept of angles of elevation.

Let's consider a right triangle formed by the ground, the tree, and a line of sight from the point on the ground to the top of the tree.

We are given:
- The distance from the front of the tree to the point on the ground is 50 feet.
- The angle of elevation from the point on the ground to the top of the tree is 48 degrees.

In a right triangle, the tangent of an angle is defined as the ratio of the length of the side opposite the angle to the length of the side adjacent to the angle.

Since we want to find the height of the tree, we need to find the length of the side opposite the 48-degree angle.

Using trigonometry, we have:

tan(48°) = height of the tree / distance from point to tree

Let's substitute the values we have:

tan(48°) = h / 50

To solve for h (height of the tree), we multiply both sides of the equation by 50:

50 * tan(48°) = h

Using a calculator, we can evaluate the tangent of 48 degrees:

50 * 1.1106 ≈ 55.53

Therefore, the height of the tree is approximately 55.53 feet.

2400

the tree is opposite the angle and the 50 feet is adjacent to the tree.

opposite/adjacent = tangent

x/50 = tan 48.

Find tan 48 and multiple by 50 to find "x" which is the height of the tree.