Answer:
The tree is 20.6 ft tall.
Step-by-step explanation:
Please check the attached graph.
From the diagram, it is clear that John is 5 ft tall is standing 20 feet away from a tree, making an angle of elevation to be 38⁰.
The diagram makes a right-angled triangle.
- Given the angle = Ф = 38⁰
- Hypotenuse = Tree length = c ?
Pythagorean Theorem:
For a right-angled triangle, with sides 'a' and 'b', the hypotenuse 'c' is defined as:
[tex]\:c=\sqrt{a^2+b^2}[/tex]
substituting a=5, b=20
[tex]c=\sqrt{5^2+20^2}[/tex]
[tex]c=5\sqrt{17}[/tex]
[tex]c=20.6[/tex] ft
Thus, the tree is 20.6 ft tall.
