Question

You are standing 200 feet from the base of a redwood tree. You estimate the angle of elevation to the top ofthe tree is 60°. What is the approximate height of the tree?

Answer 1

The distance of the person to the base tree, the height of the tree, and position of the person with respect to the top of the tree form a right angle, where the base distance is one of its legs and the height of the tree is the other leg.

To determine the height of the tree you have to use a trigonometric ratio that relates both sides of the triangle with the angle of elevation. The trigonometric ratio that relates the adjacent and opposite sides of an angle, θ, is the tangent:

`\tan \theta=(opposite)/(adjacent)`

The angle θ is the angle of elevation. (θ=60º)

The opposite side to the angle is the height of the tree. (x)

The adjacent side is the distance of the person to the base of the tree. (200ft)

So that:

`\tan 60=(x)/(200)`

Multiply both sides by 200 to determine the value of x

`\begin{gathered} 200\cdot\tan 60=x \\ x=346.41ft \end{gathered}`

The redwood tree is 346.41ft tall