Daniel stands on one side of a stream that is 400 feet wide. He wants to reach his campsite on the opposite side of the stream. The campsite is 1600 feet away from the point directly opposite where Daniel stands. He decides that he will swim to the boat ramp to get to the side of the stream the campsite is on, and then jog to the campsite. The angle formed by Daniel’s swim path and the shore at the boat ramp is 53°
1. Draw a labeled diagram of the scenario.
2. Daniel can swim at an average rate of 150 feet per minute. How many minutes does it take him to swim to the boat ramp? Round your answer to the nearest hundredth.
3 How far is the boat ramp from the campsite? Round your answer to the nearest
4. Daniel can jog at 4 miles per hour. How many minutes does it take him to jog from the boat ramp to the campsite? Round your answer to the nearest hundredth.
1. We have something like this
D
1200
B ___________ C
53°
400 

A
A = point where he stands
B = point on opposite shore directly across from Daniel
C = boat ramp
D = his campsite
2. We can find the distance he swims (A to C) as follows
Triangle ABC is a right triangle with angle ABC = 90°
And AC is the hypotenuse
And AB is the opposite side to the 53° angle
So
sin 53° = 400 / AC rearrange as
AC = 400 / sin 53 ≈ 500.85 ft
So....the time it takes to swim this distance is
500.85 / 150 ≈ 3.34 min
3. To answer this....we need to first know the distance BC.....this is given by
tan 53° = 400 / BC rearrange as
BC = 400 / tan 53° ≈ 301.42 ft
And DBC is a right triangle with hypotenuse DC.....this is the distance from the boat ramp to the campsite
So
DC = sqrt (DB^2 + BC^2)
DC = sqrt ( 1200^2 + 301.42^2 ) ≈ 1237.28 ft
4. Time it takes to jog to the campsite from the boat ramp =
Note : 4mph = 4 * 5280 / 3600 = 88/15 ft / sec
So distance / rate = time ....so....
1237.28 / (88/15) =
1237.28 * 15 / 88 = 210.9 sec ≈ 210.9/60 ≈ 3.52 min
I already answered this a couple of days ago.
And I see EP found an even earlier answer of mine.
Half the infor was missing then. On scanning this new question, some of the required info is still missing.
You did not even bother to comment on my comprehensive answer!
I guess you are just another brat here who reposts without comment when they do not get the answer that they want.
Here was my second answer