Trigonometry Question!

Question

A weather ballon is tethered to the ground at an angle of inclination equal to 30°. The string used is 400ft long. Caleb and Elissa are at different positions on level ground in line with the connection to the ground. If both Caleb and Elissa are 300ft from the balloon, how far is each from the connection to the ground?

Answer 1

Draw a figure!

There is a point directly under the balloon; it is 200*√3 feet from the tether point, i.e. 346.41 feet.

The height of the balloon is 200 feet.

The 2 observers are equidistant from this point.

The observer points form a right triangle with the balloon and this distance is sqrt(300²-200²)=223.61 feet.

Therefore, one observer is 346.41-223.61 feet from the tether point and the other is 346.41+223.61 feet from the tether point.