SOLUTION: On a day with no wind, a hot-air balloon hovers at a point above a long, straight river. On the west side of the balloon a sailboat is spotted in the river at an angle of depressio

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Question 622174: On a day with no wind, a hot-air balloon hovers at a point above a long, straight river. On the west side of the balloon a sailboat is spotted in the river at an angle of depression of 48 degrees. On the east side, a canoe spots the balloon at an angle of inclination of 29 degrees. The distance between the balloon and the canoe is 650 m.
a) What is the height of the balloon?
b) What is the distance between the balloon and the sailboat?
c) What is the distance between the sailboat and the canoe?

I really need help, thanks in advance!
Im not sure if I am solving this correctly but this is what I have done:
Sin 29 = h/650
650 x sin 29 = 315.1
Therefore the height of the balloon is 315.1 m.
B) Sin 48 = h/650
650 x sin 48 = 483.0
Therefore the distance between the balloon and the sailboat is 483m
C) 650 + 483 = 1133
Therefore the distance between the sailboat and the canoe is 1133 m
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
If you draw everything out, you'll get something like this




Note: the missing angle (up at the top) is 103 degrees since 103+29+48 = 180


You're given "The distance between the balloon and the canoe is 650 m", so you can say s = 650

This means that

sin(angle) = opp/hyp

sin(29) = h/s

sin(29) = h/650

h = 650*sin(29)

h = 315.126

So you have the right answer.

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b)

sin(48) = opp/hyp

sin(48) = h/r

sin(48) = 315.126/r

r = 315.126/sin(48)

r = 424.0438

So the distance between the balloon and the sailboat is about 424.0438 m

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c)

In this part, use the tangent function to find the values of 'x' and 'y' (see the drawing above). Then add up x and y to get the total distance between the sailboat and the canoe.