Solve the Problem $4 \sqrt { 35 } \mathrm { ft }$

Multiple Choice

Solve the problem.
-A balloon is secured to rope that is staked to the ground. A breeze blows the balloon so that the rope is taut while the balloon is directly above a flag pole that is 50 feet from where the rope is staked down. Find the altitude of the balloon if the rope is 90 feet long. Leave your answer in simplified radical form.

A) $4 \sqrt { 35 } \mathrm { ft }$
B) $10 \sqrt { 106 } \mathrm { ft }$
C) $20 \sqrt { 14 } \mathrm { ft }$
D) $2 \sqrt { 10 } \mathrm { ft }$