Boat sailing east parallel to the shore at a speed of 9 mph. At a given time, the bearing to lighthouse =S 70° E, and 30 min later = 63° E.?
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A boat is sailing due east parallel to the shoreline at a speed of 9 miles per hour. At a given time, the bearing to the lighthouse is S 70° E, and 30 minutes later the bearing is S 63° E (see figure). The lighthouse is located at the shoreline. What is the distance from the boat to the shoreline? (Round your answer to one decimal place.)
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In 30 minutes the boat has travelled 4.5 miles, thus:
d tan(70°) - d tan(63°) = 4.5
d = 4.5/[tan(70°) - tan(63°)] = 5.733 ≈ 5.7 miles
I hope this helps.
=>
sin(63°+90°) / x = sin 7° / 4.5
x = 16.7635
sin 20° = d / 16.7635
d = 5.733 miles