Problema Solution

A lighthouse is 10 km northwest of a dock. A ship leaves the dock at 9 A.M. and steams west at 12 kmh. At

what time will it be 8 km from the lighthouse?

Answer provided by our tutors

Draw the diagram. Then, Use the law of sines to find the angles where the 8 meets the west axis. 8/sin 45 = 10/sin x 8 sin x = 10 sin 45 sin x = 10 sin 45 / 8 sin x = 0.883883... x = inverse sine of that = about 62º, or 180 - 62 = 118º Now get the third angle (across from the side you need, on the west axis) in each case 180 - (45 + 62) = 73 180 - (45 + 118) = 17 Then use sine law again to get the lengths of the west axis I'll do the 17; you can do the 73: 8 / sin 45 = x / sin 17 x sin 45 = 8 sin 17 x = 8 sin 17 ÷ sin 45 x = about 3.3 km. Time = distance ÷ speed. At 12 km/h it takes 3.3/12 = 0.275 hours, times 60 = 17 minutes, so 9:17