Solving for Distance using Law of Cosines

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In summary, the ship sailing in the North Atlantic changed course at point A to a bearing of 62°, then changed course again at point C to a bearing of 115° to avoid icebergs. The distance between point A and B was 50 miles. Using the law of sines, the ship had to travel approximately 84 miles to avoid the icebergs.
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Homework Statement


A ship sailing due east in the North Atlantic has been warned to change course to avoid a group of icebergs. The captain turns at point A and sails on a bearing of 62° for a while, then changes course again at point C to a bearing of 115° until the ship reaches its original course at point B. The distance between point A and B is 50 miles. How much farther did the ship have to travel to avoid the icebergs?

Homework Equations


a2 = b2 + c2 - 2bc*cosA
b2 = a2 + c2 - 2ac*cosB
c2 = a2 + b2 - 2ab*cosC

a/sinA = b/sinB = c/sin C

The Attempt at a Solution


I figured out all of the angles, but I only have one side, and I can't get the numbers to work in any of the law of cosines equations. I don't know if I should try law of sines, because my professor told me not to use law of sines with any angles greater than 90°. I think making a system of equations in this problem would be too complicated, I'm sure there's an easier way somewhere. Help please?
 

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Oh! Nevermind, law of sines worked just fine. My professor is a poopyhead!
 

FAQ: Solving for Distance using Law of Cosines

1. What is the Law of Cosines?

The Law of Cosines is a mathematical formula used to find the missing side or angle of a triangle when two sides and an included angle are given. It is an extension of the Pythagorean Theorem and is commonly used in trigonometry and geometry.

2. How do I use the Law of Cosines to solve a triangle?

To use the Law of Cosines, you need to have two sides and an included angle of a triangle. The formula is c² = a² + b² - 2ab cos(C), where c is the missing side and C is the included angle. You can rearrange the formula to solve for any of the missing values.

3. Can the Law of Cosines be used for any triangle?

Yes, the Law of Cosines can be used for any triangle, regardless of its shape or size. However, it is most commonly used for solving oblique triangles (triangles with no right angles).

4. What is the difference between the Law of Cosines and the Law of Sines?

The Law of Cosines is used to find the missing side or angle of a triangle when two sides and an included angle are given, while the Law of Sines is used to find the missing side or angle when two angles and any side are given. The Law of Cosines is also used for solving oblique triangles, while the Law of Sines is used for solving acute or right triangles.

5. Can the Law of Cosines be used to find the area of a triangle?

No, the Law of Cosines does not directly give the area of a triangle. However, it can be used in conjunction with other formulas, such as Heron's formula, to find the area of a triangle.

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