I need help with this question:

Question

1. A hot air balloon is held at a constant altitude by 2 ropes that are anchored on the ground. One rope is 120 ft long and makes an angle of 65 with the ground. The other rope is 115 ft long. What is the distance between the points on the ground at which the 2 ropes are anchored? Round the answer to the nearest tenth of a foot.

Answer 1

I assume these ropes are on oppsite sides of the Balloon.

If so, you have two sides, one angle.

Use the law of sines to get the other ground angle.

sin65/115 =sinTheta/120

solve for sinTheta, then Theta=arcsin..

Now, since you have both ground angles, the rest is easy. You know the sum of all angles is 180, so find the angle between the ropes at the balloon.

Then, law of sin again:

sin65/115=sinTopAngle/distance
solve for distance.

You could do this problem with the law of cosines also once you know the top angle also.