Lighthouse B is 8 miles east of lighthouse A. A boat Leaves A and sails 6 miles. At this time it is sighted from B. If the bearing of the boat from lighthouse B is S71W, how far from lighthouse B is the boat?
+130466 Lighthouse B is 8 miles east of lighthouse A. A boat Leaves A and sails 6 miles. At this time it is sighted from B. If the bearing of the boat from lighthouse B is S71W, how far from lighthouse B is the boat?
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Using the law of sines, we need to first find the angle opposite the side of 8....we have
sin 19° / 6 = sin θ / 8
(8)/(6) * sin 19° = sin θ
.434 = sin θ to find θ, use the inverse sine
sin-1 (.434) ≈ 25.73°
Then the third angle (opposite the side the distance the boat is from lighthouse B) =
180 - 19 - 25.73 = 135.27° .....Then calling the distance the boat is from lighthouse B, d, we have, using the law of sines, again
d / sin 135.27° = 6 / sin 19°
d = (6) sin 135.27° / sin 19° ≈ 12.97 miles
+130466 Lighthouse B is 8 miles east of lighthouse A. A boat Leaves A and sails 6 miles. At this time it is sighted from B. If the bearing of the boat from lighthouse B is S71W, how far from lighthouse B is the boat?
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Using the law of sines, we need to first find the angle opposite the side of 8....we have
sin 19° / 6 = sin θ / 8
(8)/(6) * sin 19° = sin θ
.434 = sin θ to find θ, use the inverse sine
sin-1 (.434) ≈ 25.73°
Then the third angle (opposite the side the distance the boat is from lighthouse B) =
180 - 19 - 25.73 = 135.27° .....Then calling the distance the boat is from lighthouse B, d, we have, using the law of sines, again
d / sin 135.27° = 6 / sin 19°
d = (6) sin 135.27° / sin 19° ≈ 12.97 miles
