How Do You Solve for the Adjacent Side Using Cosine?

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In summary, the conversation discusses a right angle triangle with a hypotenuse of 10, an opposite side of 2, and an unknown adjacent side. The relevant equations include cosine and sine, and the relationship between them. It is mentioned that there are multiple ways to find the length of the adjacent side, including using the relationship between sine and cosine or using the Pythagorean theorem.
  • #1
Edobbs0916
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[Note: Image orientation fixed, image trimmed to just relevant section - gneill]

Homework Statement


hypotenuse is 10 opposite is 2 adjacent is unknown ( obviously needed for cosine)
Fig2.gif


Homework Equations


Cosine= adjacent/hypotenuse
Sine=opposite/hypotenuse

The Attempt at a Solution

 

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  • #2
Hello edobbs0916, Welcome to Physics Forums.

Your post would be better placed in the Precalculus Mathematics Homework forum, so I have moved it there.

Also, as a hint, in a right angle triangle if you have two sides you can always calculate the third. So you need one more Relevant Equation...
 
  • #3
There are plenty of options here.
In the image, it seems like you have already found the length of the adjacent side (rounded improperly). So you could just go with what you know and check your arithmetic.
You could also use the relationship that ## \sin^2\theta + \cos^2\theta = 1## for any angle ##\theta##, so if you know sin, you can quickly know cos.
 

Related to How Do You Solve for the Adjacent Side Using Cosine?

1. What is cosine and how is it used in problem solving?

Cosine is a trigonometric function that represents the ratio of the adjacent side of a right triangle to its hypotenuse. In problem solving, cosine is used to find missing sides or angles in a right triangle.

2. How do I find the cosine of an angle?

To find the cosine of an angle, you can use a calculator or a trigonometric table. Simply input the angle measure in degrees or radians and press the cosine button on your calculator or find the corresponding value in the table.

3. How do I use cosine to solve a problem?

To solve a problem using cosine, you first need to identify the given information and what you are trying to find. Then, you can use the cosine function (cos) and its inverse (arccos) to find the missing side or angle.

4. Can I use cosine in non-right triangles?

No, cosine can only be used in right triangles. For non-right triangles, you can use other trigonometric functions such as sine and tangent.

5. What are some common mistakes to avoid when using cosine?

One common mistake is using the wrong angle or side in the cosine function. Make sure to label your triangle correctly and use the appropriate angle or side in the function. Also, be careful when using inverse cosine (arccos) as it may give multiple solutions.

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