The height of the tree is 8.3 ft.
To solve this problem, we have to find the angle of elevation from the student.
To do this, we have to assume or bring out a right angle triangle and solve for the.
Given that we have the distance of A to F and the point to F
- A to F = 5ft
- E to F = 6
- angle ?
Trigonometric Ratio
Using trigonometric ratio,
We can find the tangent of this angle
[tex]tan\theta = \frac{opposite}{adjacent} \\tan\theta = \frac{6}{5}\\ tan \theta = 1.2\\\theta = tan^-^1(1.2)\\\theta = 50.2^0[/tex]
The angle of elevation can be calculated using sum of angles in a triangle is equal to 180 degrees
[tex]180 = 90 + 50.2 + x\\x = 180- 140.2\\x = 39.8^0[/tex]
Assuming a right angle triangle from the point the student is standing, the distance from him to the tree would be
[tex]15 - 5 = 10ft[/tex]
Let's use the tangent of the angle to find the height of the tree.
[tex]tan\theta = \frac{opposite}{adjacent} \\tan 39.8 = \frac{x}{10}\\x = 10 tan39.8\\x = 8.3ft[/tex]
From the calculations above, the height of the tree is 8.3 ft.
Learn more on trigonometric ratio here;
https://brainly.com/question/10417664
