# Balloon problem

#### Zhowers

##### New member
So halfway through the problem I noticed that the problem could have been used as a law of cosines, and I feel like I might be wrong so far. I'm pretty stuck and would appreciate any help! Thank you.

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#### HallsofIvy

##### Elite Member
Let the tension in the left rope be $$\displaystyle T_1$$ and the tension in the right rope be $$\displaystyle T_2$$. Draw a line straight down from the balloon. That divides the problem into two right triangles. On the left we have a hypotenuse of "length" $$\displaystyle T_1$$ and angle 60 degrees. The vertical component of force is $$\displaystyle T_1 sin(60)$$, downward, and horizontal component of force is $$\displaystyle T_1 cos(60)$$, to the left. On the right we have a hypotenuse of "length" $$\displaystyle T_2$$ and angle 25 degrees. The vertical component of force is $$\displaystyle T_2 sin(25)$$, downward, and horizontal component of force is $$\displaystyle T_2 cos(25)$$, to the right.

The total horizontal force must be 0: $$\displaystyle T_1cos(60)= T_2cos(25)$$. The total vertical force is also 0 but that exerted by the ropes must offset the upward lifting force, 570 pounds: $$\displaystyle T_1sin(60)+ T_2sin(25)= 570$$. Solve those two linear equations for $$\displaystyle T_1$$ and $$\displaystyle T_2$$.