Introduction to the Law of Cosines Calculator:
Law of cosines calculator is an online tool that is used to find the law of cosines of a given function. It helps to simplify the process of finding the cosine angle and cosine length of a triangle's sides in a few seconds.
Cosine rule calculator is a reliable tool as it gives you an accurate solution of the law of the cosine problems of a triangle without doing any manual calculation which means its evaluation process is free from human error.
What is the Law of Cosine?
A Law of Cosines is a trigonometric process that is used to solve problems of the sides and angles of a given triangle. It is useful for non-right angle triangles but you can use it to solve for right angle triangles as well.
This method is useful when the Pythagorean theorem does not apply to solving these types of questions. The law of cosine process is used in engineering, navigation, and physics where the measurement of angle is important.
Law of Cosines Formula:
The law of cosines formula consists of the side of the length value of a,b, and c while C is the angle opposite the side of the given triangle. The law of cosines equation used by the law of cos calculator is,
$$ cos (C) \;=\; \frac{a^2 + b^2 - c^2}{2ab} $$
How to Calculate the Law of Cosine?
To calculate the cosine rule function value, the law of cosines solver uses formal steps to simplify given functions. you need to know about the basic property of the cosine function of geometry.
Step 1:
Identify the given data from the triangle function for the law of cosine function.
Step 2:
First, find the third length or side of the triangle if you have given two sides of the triangle.
$$ a^2 \;=\; b^2 + c^2 - 2bc\; cos\; A $$
Step 3:
Now you can modify the formula to find the angle value of the triangle using the given value of sides a,b, and c.
$$ cos (C) \;=\; \frac{a^2 + b^2 - c^2}{2ab} $$
Step 4:
After finding the value of the second angle you can use the area of the triangle formula which is given to find the third angle value.
$$ A + B + C \;=\; 180 $$
Practical Example of the Law of Cosine:
The law of cosines calculator is used to calculate the cosine value easily but to understand the calculating process manually you need to know its solving method. So, an example of the law of cosine function is given below,
Example: solve the triangle Δ ABC given A = 30°, b = 4 and c = 5.
PASTE THE GRAPH HERE!
Solution:
As the given data is an angle A = 30 and the length of the sides b = 4, c = 5.
To find the third side c we can modify the formula of the law of cosine according to given values,
$$ a^2 \;=\; b^2 + c^2 - 2bc\; cos\; A $$
Put the values in the above formula and simplify it.
$$ a^2 \;=\; b^2 + c^2 - 2bc\; cos\; A $$
$$ =\; 4^2 + 5^2 - 2(4)(5)\; cos 30° \;=\; 6.36 ⇒ a \;=\; 2.52 $$
For the angle of B again modify the formula which is given as:
$$ b^2 \;=\; c^2 + a^2 - 2ca\; cos\; B ⇒ cos\; B \;=\; \frac{c^2 + a^2 - b^2}{2ca} $$
Put the values in it and simplify the expression to get the angle value of B.
$$ ⇒ cos\; B \;=\; \frac{5^2 + (2.52)^2 - 4^2}{2(5)(2.52)} \;=\; 0.6091 $$
$$ ⇒ B \;=\; 52.5° $$
Lastly, for the value of angle C use the triangle formula which is,
$$ A + B + C \;=\; 180 $$
$$ C \;=\; 180 - A - B $$
$$ C \;=\; 180 - 30 - 52.5 $$
$$ C \;=\; 97.5° $$
How to Use Cosine Rule Calculator?
Law of cosines solver has a simple layout that allows everyone or even a beginner can use it to calculate the law of cosine problems.
Before adding the value in law of cosines calculator you need to follow our instructions. These instructions are:
- Enter the sides of the length of the cosine triangle input field.
- Enter the angle of the cosine triangle in the input field of cosine law calculator.
- Recheck your law of cosine value before clicking on the calculate button.
- Click the “Calculate” button to get the desired result of a law of cosine value question.
- If you are trying our law of cosine calculator for the first time then you can use the load example so that you get better clarity about its calculation procedure.
- Click on the “Recalculate” button to get a new page for solving more laws of cosine value problems.
Output from Law of Cosines Solver:
Law of cos calculator gives you the solution to your law of cosine questions when you provide the input value to it. It provides you with solutions which may contain as,
- The laws of cosine calculator result option gives you a solution for the law of function cosine questions.
- The possible step provides you with all the steps where a complete process is given for finding the law of cosine value questions.
Advantages of Law of Cosine Calculator:
Cosine law calculator gives you multiple advantages whenever you use it to calculate the law of cosine problems and get results quickly without any external assistance. These advantages are:
- This calculator takes much time to calculate the law of cosine value problems solution especially when you do work manually but our tool can save you time and effort.
- The law of cos calculator is a free-of-cost tool so you can use it for free to find the law of cosine function value problems with solutions without a fee.
- This is a handy tool that allows you to solve the law of cosine problems and gives you exact solutions as per your input value of side length and angle.
- You can use this calculator for practice to get familiar with the concept of law of cosine function questions.
- The law cosines calculator is a trustworthy tool that provides you with precise solutions every time whenever you use it to find a law of cosine problems of triangles without any error.
- Cosine rule calculator is a user-friendly tool that you can use for evaluation of the sides and angles of the triangle, so you do not need to become an expert.
