Question

Martha is in a hot air balloon that has risen straight up from the launch point. Matthew isstanding on the ground 16 meters away from the launch point. If Martha and Matthew are 20meters apart, how high has the balloon risen?

Answer 1

Let the height of the balloon be h.

The problem is illustrated in the diagram below:

Notice that the distances form sides of a right triangle. Apply the Pythagorean theorem to the triangle:

`h^2+16^2=20^2`

Solve the equation for h:

`\begin{gathered} h^2+256=400 \\ \Rightarrow h^2=400-256 \\ \Rightarrow h^2=144 \\ \Rightarrow h=√(144)=12 \end{gathered}`

The balloon has risen to a height of 12m.