What is the missing angle using Law of Cosines?

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In summary, the conversation discusses using the Law of Cosines to find an angle and how to continue solving for the angle using the inverse function of cosine. The final step is to find the arc-cosine of the given number, in this case 0.999, to find the angle.
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Homework Statement



I am looking for an angle, using Law of Cosines. I am trying to solve for C.

Homework Equations



R^2= a^2+b^2- (2 X a X b X cos C)

The Attempt at a Solution



These are the numbers I am using, plugged into the Law of Cosines:
80^2= 450^2+ 373^2-(2 X 450 X 373 X cos C)
I have solved this far, Cos C= -.999
I know it's right this far, because my teacher told me it was, but I don't know how to find the angle past this point. I know I have to use inverse of cosine somehow. Please, help me, test tomorrow. Thanks.:)
 
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  • #2
The cosine of an angle will give you a number (a fraction, actually) that will be between zero and 1.0 .

If you have that number (0.999 as is the case here) then you find the angle by using the inverse function. Properly, it is called the "arc-cosine" but the calculators these days use the "cos^-1" symbol.

Simply find the cos^1 of 0.999 . It's going to be a small angle, less than 5 degrees.
 

Related to What is the missing angle using Law of Cosines?

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 known. It is an extension of the Pythagorean theorem.

How do you use the Law of Cosines?

To use the Law of Cosines, you first need to identify which side or angle is missing. Then, plug in the known values into the formula: c² = a² + b² - 2ab cos(C), where c is the missing side, a and b are the known sides, and C is the included angle. Finally, solve for the missing side or angle using algebraic methods.

When do you use the Law of Cosines?

The Law of Cosines is typically used when the given information about a triangle does not fit the criteria for using the Pythagorean theorem. This includes cases where all three sides are known, or when two sides and the included angle are known.

What are the limitations of the Law of Cosines?

The Law of Cosines can only be used to solve for missing sides and angles in triangles, specifically for acute and obtuse triangles. It cannot be applied to other shapes, such as quadrilaterals or circles.

How does the Law of Cosines relate to real-world applications?

The Law of Cosines is used in various fields, such as engineering, physics, and navigation. It can be applied to solve problems involving distance and direction, such as calculating the displacement of an object or determining the location of a point based on known distances and angles.

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