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 depressi
Algebra.Com
Question 1058536: 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 650m.
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?
My solutions:
Divide triangle BSC into two right angle triangles by drawing a line between angle B (the top) down to the base (line SC) and calling it h and the point where it meets SC as point D. Angle C
is 29 degrees, length BC is 650m, angle S is 48 degrees. Length BS is c.
a) Solving for h (height) sine theta in triangle BCD:
sin(29) = opposite/hypotenuse
sin(29) = h/650
h = 650sin(29)
h = 315.1 meters
b) sin(48) = opposite/hypotenuse in triangle BDS
sin(48) = 315.1/c
c = 315.1/sin(48)
c = 424 meters
c) finding length of SD
tan(48) = 315.1/SD
SD = 315.1/tan(48)
SD = 283.7
finding length DC
tan(29) = 315.1/DC
DC = 315.1/tan(29)
DC = 568.5
283.7 + 568.5 = distance between sailboat and canoe is 852.2 meters.
Am I right?
Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
Yes. The cos (29)=x/650, and I get 568.5 m. All the other calculations are correct. Well done.
RELATED QUESTIONS
On a day with no wind, a hot-air balloon hovers at a point above a long, straight river.... (answered by jim_thompson5910)
A hot air balloon is floating above a straight road. To estimate their height above the... (answered by mananth)
Triangle A, B and C are three points on a horizontal field. A is due west of B, the... (answered by CPhill)
A hot-air balloon is floating above a straight road. To estimate their height above the... (answered by Alan3354)
a hot air balloon is floating above a straight road. To estimate their height above the... (answered by lynnlo)
A hot air balloon is to be attached to the ground using two support ropes. One support is (answered by mananth)
Two observers on the ground are 2000m apart. Observer A measures the angle of elevation... (answered by rothauserc)
A man started from a certain A man started from a certain point and travelled in a... (answered by ikleyn,Alan3354)
A hot-air balloon is flying at an altitude of 2687 feet. If the angle of depression from... (answered by ikleyn)