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# Law of sines problem. I think I got the answers 78.6229 and 101.3771 but I’m not sure if I interpreted the wording correctly.

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Law of sines problem. I think I got the answers 78.6229 and 101.3771 but I’m not sure if I interpreted the wording correctly.

Nov 17, 2018

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Deleted.

Nov 17, 2018
edited by Guest  Nov 17, 2018
edited by Guest  Nov 17, 2018
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We have a SSA-type problem

Let the lighthouse be located at C......angle ACB  = 33°

C

36

A        20        B

We are looking for angle CBA

We can find angle CAB, first

Using the Law of Sines

sin ACB /20 = sinCAB / 36

sin (33) / 20  = sin(CAB) /36

(36/20)sin (33)  = sinCAB

arcsin [ (36/20)sin(33)] = CAB  ≈ 78.62°

Therefore  a possible value for  angle CBA   ≈ 180 - 33 - 78.62  ≈ 68.38°

Another possible value for angle CAB  =  180 - 78.62  ≈ 101.38°

Add  this to the known angle ACB  =  33 + 101.38   = 134.38°

Because this is < 180, we have two possible triangles

So....the other possible value for angle CBA  = 180 - 134.38  = 45.62°

Nov 17, 2018