Questions on Geometry: Triangles answered by real tutors!

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Question 152285: Two boats leave the port at the same time. The first boat travels due east at 14 mph, and the second boat travels at 28 mph in the direction of N30 degrees east.
To the nearest tenth of a mile, how far apart will the boats be in a half an hour? (Distance = (Rate)(Time), 0.5 represents a half an hour.): Two boats leave the port at the same time. The first boat travels due east at 14 mph, and the second boat travels at 28 mph in the direction of N30 degrees east.
To the nearest tenth of a mile, how far apart will the boats be in a half an hour? (Distance = (Rate)(Time), 0.5 represents a half an hour.)
Answer by jojo14344(832) About Me  (Show Source):
You can put this solution on YOUR website!
Okay, let's make distance of 1st boat as D[1] going EAST, and 2nd boat as D[2] going N30deg EAST. In solving ofr D[1] and D[2] you already gave the formula, D=(rate)(time).
So in half an hour,
D[1]=(14mi/cross(hr))(0.5cross(hr))
D[1]=7miles
D[2]=(28mi/cross(hr))(0.5cross(hr))
D[2]=14miles
Now, we appoint D[3] as the distance of the 2 boats, AND D[1], D[2], & D[3] FORMS A RIGHT TRIANGLE W/ ANGLE 30 DEGREES.
You have 2ways of solving this, by PYTHAGOREAN THEOREM or TRIGO FUNCTIONS.
By Pyth Theorem,
D[2] forms the hypotenuse, D[1] as the adjacent side, and D[3] as the opposite side:
D[2]^2=D[1]^2+D[3]^3
D[3]^2=D[2]^2-D[1]^2
D[3]=sqrt(14^2-7^2)=sqrt(147)
D[3]=12.12miles ----------------> dist bet the boats after 1/2 hour
Or By TRIGO FUNCTIONS:
sin(alpha)=D[3]/D[2]= opp/hyp
D[3]=sin(60)*14miles
D[3]=12.12miles ---------------. dist bet 2 boats after 1/2 hour
Why 60 degrees?
North & East directions are like xy coordinates that forms 90 deg. Since 30 deg is given on the north side, the other 60 deg we used on the east side since we're referring on the 1st boat on the east direction.
Hope this help.
Thank you,
Jojo