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Ship A and Ship B are 120 km apart when they pick up a distress call from another boat. Ship B estimates that they are 70 km away from the distress call. They also notice that the angle between the line from ship B to ship A and the line from ship A to the distress call is 28°. What are the two possible distances, to the nearest TENTH of a km, from ship A to the boat?

User Ismael
by
8.5k points

1 Answer

3 votes

Answer:

147.5 km and 64.4 km

Explanation:

a=120 km

b=70 km

β=28 degrees ( ∘)

b^2=(a^2)+(c^2)−2ac*cosβ

70^2 =(120^2 )+(c^2)−2⋅ 120⋅ c⋅ cos(28∘ )

(c^2 ) −211.907c+9500=0

note p, q, and r are replacement variables in the Pythagorean theorem since a, b, and c are already in use

p=1;q=−211.907;r=9500

D=(q^2 ) −4pr=(211.907^2 )−4⋅1⋅9500=6904.75561996

D>0


c_(1,2) = (−q±
√(D) )/2p=(211.91±
√(6904.76))/2


c_(1,2) =105.95371114±41.5474295834

(
c_(1)−147.501140726)(
c_(2)−64.4062815596)=0


c_(1)=147.501140726


c_(2)=64.4062815596

User Mshnik
by
7.5k points

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