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# Trigonometry: Further Applications of Right Triangles

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Hello! I am in an online trigonometry class and we currently have an assignment that asks us to solve this problem. I am slightly confused about it and where to even start. Any assistance on the process to solve this would be so greatly appreciated.

The problem goes as follows:

Two docks are located on an east-west line 2590 feet apart. From dock A, the bearing of a coral reef is 62°24′. From dock B, the bearing of the coral reef is 332°24'. Find the distance from dock A to the coral reef.

The distance from dock A to the coral reef is __ feet. (Round to the nearest integer as needed.)

Thank you for your help in advance. It means alot to me. :)

Sep 17, 2018

### 1+0 Answers

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A bearing of 62.24° converts to an angle of 90 - 62.24 = 27.76°

And a bearing of  332.24°  converts to an angle of 332.24 - 270  = 62.24°

So we have a triangle  with angles of  27.76° and  62.24°

And the third angle of the triangle is  180 - 27.76 - 62.24  = 90°

So....we can find the distance from A to the coral reef using the Law of Sines

2590 / sin 90  =  D /  sin 62.24      where D is the distance we want

2590 / = D / sin 62.24       multiply both sides by sin62.24

2590 * sin 62.24  =  D ≈ 2292 ft.

Here's the approximate picture....dock "A" is a (0,0)....the reef is point B...and  dock "B"  is at point C

Sep 17, 2018