Last angle problem!?

Question

Two people are walking towards each other on a path in a park. The path runs east and west. A hot air balloon is directly above the path betwen them. One of the walkers sees the balloon when looking east at an angle of eleation of 46 degrees. The other walker sees the balloon looking west at an angle of elevation of 72 degrees. If the walkers are 55 yards appart, how far is the balloon fron the 2nd observer? (to the nearest hundredth)
Please explain how to sketch and step by step how to solve.

Answer 1

you would sketch a triange with points at the runners and the balloon and the angles that you are given would be between each of the runners and the balloon. You can find the angle at the balloon by 180 - 46-72 = 62.

The base of the triangle (between the runners) is 55 yards.
Now you can find the lengths of all other side with the law of sins (A/sina = B/sinb = C/sinc) where A,B,C are side lengths and a,b,c are opposing angles. Now you have the answer.

Answer 2

Hey, yumiyum, this is pretty much like your problem with the angle of elevation from the building with two sightings. In this case, the two sighting are from opposite sides of the balloon.
So the west-side observer equation is
Tan 46 = height/distance to balloon.
We'll call that distance x
The east-side observer equation is
Tan 72 = height/distance to balloon.
This distance is 55-x. This is what we want to find out.
Again, you find the tan values, and solve two equations for x.

Answer 3

While I would love to help, I suggest you do your own homework. If you learned this in school, why not call a classmate that knows what your teacher expects from you? If you need more help, talk to your teacher and don't be afraid to ask for help. If you don't feel like doing your homework, don't do it and take the zero. You can get suspended or even expelled from school if it was found out that you did not do your own homework. Just trying to help! ;-)