Question

John who is 5 ft tall is standing 20 feet away from a tree, and you measure the angle of elevation to be 38∘. How tall is the tree? Find your answer to the nearest tenth

Answer 1

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

• Adjacent = a = 5 ft

• Opposite = b = 20 ft

• Hypotenuse = Tree length = c  ?

Pythagorean Theorem:

For a right-angled triangle, with sides 'a' and 'b', the hypotenuse 'c' is defined as:

$\:c=\sqrt{a^2+b^2}$

substituting a=5, b=20

$c=\sqrt{5^2+20^2}$

$c=5\sqrt{17}$

$c=20.6$ ft

Thus, the tree is 20.6 ft tall.