Law of Cosines Calculator

Select the parameter you wish to calculate and enter the required ones in the respective fields. The tool will use the law of cosine to determine the results instantly.

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Calculate:

Side a:

m ▾

Side b:

cm ▾

Side c:

cm ▾

$ A = \cos^{-1} \left[ \dfrac{b^2+c^2-a^2}{2bc} \right] $

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This regulation of cosines calculator will assist you to calculate the perimeters and angles of a triangle appropriately. you may calculate all other last aspects and degree angles in a triangle with the aid of the use of specific types of cosine law.

what's the regulation of Cosines?

The law of cosines is a group of formulas that relates the period of sides of a triangle to one of its cosine angles. The cosine regulation is normally desired whilst 3 sides of a triangle are given for finding any angle A, B, or C of the triangle or the two adjacent aspects and one perspective is given.

The law of cosines components is a form of Pythagorean Theorem which tailored to be used of non-right triangle, but the Pythagorean Theorem most effective works for right triangles. So, you can use the regulation of cosine calculator triangle that applies the regulation of cosines to locate attitude and facets in moments.

Law of Cosines formulation:

If the period of sides is a, b, and c contrary to the angles A, B, and C are given, then the regulation of cosine expresses: $a^2=b^2+c^2−2 \text{ b c } cos(A)$ $b^2=a^2+c^2−2 \text{ a c } cos(B)$ $c^2=a^2+b^2−2 \text{ a b } cos(C)$

Law of Cosines For sides a, b, and c:

with a view to locate any side of a triangle the law of cosines components transforms in case you know two lengths of facets and the measures of an perspective that's opposite to one among them. $a=\sqrt{b^2+c^2−2 \text{ b c } cos(A)}$ $b=\sqrt{a^2+c^2−2 \text{ a c } cos(B)}$ $c=\sqrt{a^2+b^2−2 \text{ a b } cos(C)}$ also, if the 2 lengths of aspects and angle are regarded, then definitely add the values into the law of cosines sas calculator, and permit it carry out calculations.

Law of Cosines For Angles A, B, and C:

In case you realize 3 sides of a triangle then you could use the cosine rule to find the angles of a triangle. So, the solving formula for the angles that are utilized by the law of cosines formula is $A=cos^{−1}[\frac{b^2+c^2−a^2}{2bc}]$ $B=cos^{−1}[\frac{a^2+c^2−b^2}{2ac}]$ $C=cos^{−1}[\frac{a^2+b^2−c^2}{2ab}]$

Example:

In triangle (∠ ABC)

Side a = 7 cm
Side b = 8 cm
Side c = 12 cm

Find the largest angle.

Solution:

The largest angle of a triangle is facing the longest side, C:

$$ c^2 = a^2 + b^2 - 2ab \cdot \cos C $$

Rearranging for $ \cos C $:

$$ \cos C = \frac{a^2 + b^2 - c^2}{2ab} $$

Substitute the values:

$$ \cos C = \frac{7^2 + 8^2 - 12^2}{2(7)(8)} $$

$$ \cos C = \frac{49 + 64 - 144}{112} $$

$$ \cos C = \frac{-31}{112} $$

$$ \cos C = -0.2768 $$

Now find the angle $ C $ using the inverse cosine function:

$$ C = \cos^{-1}(-0.2768) $$

$$ C \approx 106.1^\circ $$

So, the largest angle of triangle ABC is $ C \approx 106.1^\circ $.

However, an online Law Of Sines Calculator helps you to find the unknown angles and lengths of sides of a triangle.

How law of Cosines Calculator Works?

The regulation of cos calculator lets you locate all unknown missing values of a triangle by way of using the following steps: input:

First, you need to pick a side or an attitude of the triangle that is required from the drop-down menu, then the calculator displays the corresponding form of the law of cosines formula.
Now, placed all the values into a associated field.
Then, choose the correlated units.
After putting all values click the calculate button.

Output:The law of cosines calculator presentations the subsequent results by way of the usage of the regulation of cosine components: