Answer to Question #139617 in Trigonometry for Raffy

Question #139617
From a ship two lighthouses bear N 40o
E. After the ship has sailed 15 miles on a course of 135o
, they bear
10o
and 345o
, respectively. Find the distance between the two lighthouses.
1
Expert's answer
2020-10-22T17:46:32-0400

"S_0S_1=15" (miles)

"\\angle L_1S_0N_0=\\angle L_2S_0N_0=40\\degree"

"\\angle L_2S_0P=50\\degree"

"\\angle N_0S_0S_1=135\u00b0"

"\\angle L_2S_0S_1=135\u00b0-40\u00b0=95\u00b0"

"\\angle L_1S_1N_1=10\u00b0"

"\\angle N_1S_1L_2=360\u00b0-345\u00b0=15\u00b0"

"\u2206TPS_1: \\angle TPS_1=90\u00b0-15\u00b0=75\u00b0=\\angle L_2PS_0"

"\u2206PL_2S_0:\\angle PL_2S_0=180\u00b0-\\angle L_2PS_0-\\angle L_2S_0P=180\u00b0-75\u00b0-50\u00b0=55\u00b0"

"\u2206L_2L_1S_1: \\angle L_2L_1S_1=\\angle S_0L_2S_1-\\angle L_2S_1L_1=55\u00b0-25\u00b0=30\u00b0"


"\u2206S_0L_2S_1: \\frac{S_1L_2}{sin95\u00b0}=\\frac{S_0S_1}{sin55\u00b0}"

"S_1L_2=S_0S_1\\frac{sin95\u00b0}{sin55\u00b0}"


"\u2206S_1L_1L_2: \\frac{L_1L_2}{sin25\u00b0}=\\frac{S_1L_2}{sin30\u00b0}"

"L_1L_2=S_1L_2\\frac{sin25\u00b0}{sin30\u00b0}=S_0S_1\\frac{sin95\u00b0}{sin55\u00b0}\\cdot \\frac{sin25\u00b0}{sin30\u00b0}\\approx15.42" (miles)


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Comments

Assignment Expert
23.10.20, 19:51

Dear Raffy, You are welcome. We are glad to be helpful. If you liked our service, please press a like-button beside the answer field. Thank you!

Raffy
23.10.20, 01:05

Excellence

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