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

The tree is 20.6 ft tall.

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=√(a^2+b^2)`

substituting a=5, b=20

`c=√(5^2+20^2)`

`c=5√(17)`

`c=20.6` ft

Thus, the tree is 20.6 ft tall.