Question

There are many ropes keeping a hot air balloon from floating away before a balloon race. One of these ropes is fixed to the ground at a 45° angle. Another is fixed to the ground at a 30° angle. If the hot air balloon is 15 feet off the ground, what is the distance between the two ropes rounded to the nearest hundredth of a foot?

Answer 1

\[15\sqrt{3}-15\]

Answer 2

for the triangle with 45 degree angle the distance from the perpendicular is 15 (same as perpendicular)
for the triangle with 30 degrees you can use either tan or sine
using sine of 30 degrees = 1/2 the hypotenuse is 30 and the other leg is
\[\sqrt{30^{2}-15^{2}}\]
which is approximately 25.9808