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Answered

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Problem: Two towns, A and B, located along the coast of the Pacific Ocean are 30
km apart on a north-south line. From a ship, the line of sight of town A is W30°N,
while that of town B is S400W.
1. How far is the ship from town A?
2. How far is the ship from town B?
​

NenProblem Two Towns A And B Located Along The Coast Of The Pacific Ocean Are 30km Apart On A Northsouth Line From A Ship The Line Of Sight Of Town A Is W30Nwhi class=

Sagot :

Answer:

Step-by-step explanation:

From the picture attached,

m∠COB = 90° - m∠BOS

              = 90° - 40°

              = 50°

tan(30°) = [tex]\frac{AC}{OC}[/tex]

[tex]\frac{1}{\sqrt{3}}=\frac{AC}{OC}[/tex]

AC = [tex]\frac{OC}{\sqrt{3}}[/tex]  ------(1)

Similarly, tan(50°) = [tex]\frac{BC}{OC}[/tex]

BC = OC[tan(50°)] -------(2)

Now AC + BC = 30 cm

By substituting the values of AC and BC from equation (1) and (2),

[tex]\frac{OC}{\sqrt{3}}+OC(\text{tan}50)=30[/tex]

(1.769)OC = 30

OC = 16.96

1). cos(30°) = [tex]\frac{OC}{AO}[/tex]

[tex]\frac{\sqrt{3}}{2}= \frac{16.96}{OA}[/tex]

[tex]OA=19.58[/tex] cm

Therefore, distance between the ship and town A is 19.58 cm.

2). cos(50°) = [tex]\frac{OC}{OB}[/tex]

0.6428 = [tex]\frac{16.96}{OB}[/tex]

OB = 26.38 cm

Therefore, distance between the ship and town B is 26.38 cm.

View image eudora
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