SOLUTION: A hot-air balloon is held at a constant altitude by two ropes that are anchored to the ground. One rope is 130 feet long and makes an angle of 55° with the ground. The other rope i

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Question 1073304: A hot-air balloon is held at a constant altitude by two ropes that are anchored to the ground. One rope is 130 feet long and makes an angle of 55° with the ground. The other rope is 125 feet long. What is the distance between the points on the ground at which the two ropes are anchored? (Enter your answers as a comma-separated list. Round your answers to the nearest whole number.)
Found 2 solutions by josgarithmetic, MathTherapy:
Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
The two ropes are hypotenuses of two right triangles which share a common leg which is the height of the balloon above the ground.

130 foot rope:
130%2Acos%2855%29, distance from point below the balloon to rope connection point


Height of balloon:
130%2Asin%2855%29

125 foot rope:
Let x be the distance from point below the balloon to this rope's connection point.
x%5E2%2B%28130%2Asin%2855%29%29%5E2=125%5E2
You want to solve this for x.


What you want to finish evaluating is
x%2B130%2Acos%2855%29

Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!
A hot-air balloon is held at a constant altitude by two ropes that are anchored to the ground. One rope is 130 feet long and makes an angle of 55° with the ground. The other rope is 125 feet long. What is the distance between the points on the ground at which the two ropes are anchored? (Enter your answers as a comma-separated list. Round your answers to the nearest whole number.)
1) Use LAW of SINES to determine the angle that the 125-ft rope makes with the ground.

2) Subtract the angle in 1) to determine the angle the 2 ropes makes with each other. 

3) Use the angle the ropes makes with each other, any other known angle and its opposite side, 

   and the LAW of SINES to determine the distance between the anchor-points on the ground.