Question

a light house is 10 miles northeast of a dock. A ship leaves the dock at noon and sails east at a speed of 12 miles an hour. At what time will it be 8 miles from the light house? please help me

Answer 1

@ShadowLegendX

Answer 2

@dan815

Answer 3

sine law is sinA/a = sinB/b = sinC/c
NE is 45 degrees which we'll call Angle A

at the desired configuration, a = 8 miles
and the light house to dock distance c = 10 miles

we can then figure the angle C the ship sees between the dock and the light house

sin45/8 = sinC/10
sinC = 10(sin45/8)
sinC = .884
C = 62.1 degrees or 117.9 degrees

As the three internal angles of a triangle =180 = A + B + C
the third angle becomes either B=72.9 or B= 17.1

Plugging back into sine law to figure distance ship b has traveled
sin 17.1/b = sin 117.9/10
b=10 sin 17.1/sin117.9
b= 3.33 miles
or
sin72.9/b=sin62.1/10
b=10sin72.9/sin62.1
b=10.82 miles

so the first lapsed time is (3.33/12)60 = 16.65 minutes later or 12:16:39
the second lapsed time is (10.82/12)60 = 54.1 minutes later or 12:54:06

Answer 4

anyone can show me the figure or given for this :D