Short Answer 
The total height of the tree is approximately 23.84 feet, calculated using the tangent function with the information that a student stands 20 feet away from the tree and looks up at a 50-degree angle, with their eyes 5 feet above the ground.
Step 1: Understand the Situation
To determine the height of the tree, we start by analyzing the given information. A student stands 20 feet away from the base of the tree and looks up at an angle of 50 degrees. It is also important to note that the student’s eyes are 5 feet above the ground, which will be factored into our calculations.
Step 2: Apply the Tangent Function
We can use the tangent function from trigonometry, which is defined as the ratio of the opposite side to the adjacent side in a right triangle. In this case, we set up the equation using the known distances:
- Let h represent the height of the tree above the student’s eye level.
- The adjacent side (distance from the tree) is 20 feet.
- The angle of elevation is 50 degrees.
- The equation becomes: tan(50) = (h + 5)/20.
Step 3: Solve for the Height
To find the total height of the tree, we will solve the equation for h. First, we cross-multiply and isolate h:
- Cross-multiply: h + 5 = 20 √ó tan(50).
- Calculate: h = 20 tan(50) – 5.
- This yields approximately: h = 18.84 feet.
- Add the height of the student’s eyes: Total height = 18.84 + 5 = 23.84 feet.