SOLUTION: Two ships leave the docks D, at the same time Pricess pearl P, sales on a baring of 160 degrees at a speed of 18 km/hour and a Regal rose R, sales on abearing of 105 degrees. After

Algebra ->  Triangles -> SOLUTION: Two ships leave the docks D, at the same time Pricess pearl P, sales on a baring of 160 degrees at a speed of 18 km/hour and a Regal rose R, sales on abearing of 105 degrees. After      Log On


   

Question 935601: Two ships leave the docks D, at the same time Pricess pearl P, sales on a baring of 160 degrees at a speed of 18 km/hour and a Regal rose R, sales on abearing of 105 degrees. After two hours the angle DRP is 80 degree.
Find
a- The distance between the ships at this time.
b- The speed of the regal rose.
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
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Two ships leave the docks D, at the same time Princess Pearl P, sails on a bearing of 160 degrees at a speed of 18 km/hour and a Regal rose R, sales on a bearing of 105 degrees.
After two hours the angle DRP is 80 degree.
:
Draw at triangle DPR,
side DP: 2*18 = 36 km
Angle D: 160-105 = 55 degrees
Angle R: Given as 80 degrees
Angle P: 180-55-80 = 45 degrees
Find
a-The distance between the ships at this time
Let d = distance between the ship R to P
Use the law of sines
d%2Fsin%2855%29 = 36%2Fsin%2880%29
find the sines and cross multiply
.985d = .819*36
d = 29.49/.985
d = 29.9 km apart
:
b- The speed of the Regal Rose
let p = the distance traveled by the Regal Rose
p%2Fsin%2845%29 = 36%2Fsin%2880%29
.985p = .707*36
p = 25.452 km
Find the speed
25.452/2 = 12.7 km/hr