Cos C given Three Sides of Triangle Calculator

✖The Side A of Triangle is the length of the side A, of the three sides of the triangle. In other words, the side A of the Triangle is the side opposite to the angle A.ⓘ Side A of Triangle [S_a]			+10% -10%
✖The Side B of Triangle is the length of the side B of the three sides. In other words, the side Bof the Triangle is the side opposite to the angle B.ⓘ Side B of Triangle [S_b]			+10% -10%
✖The Side C of Triangle is the length of the side C of the three sides. In other words, side C of the Triangle is the side opposite to angle C.ⓘ Side C of Triangle [S_c]			+10% -10%

✖Cos C is the value of the trigonometric cosine function of the angle C of the triangle.ⓘ Cos C given Three Sides of Triangle

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Formula

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Cos C given Three Sides of Triangle

Formula

`"cos C" = ("S"_{"a"}^2+"S"_{"b"}^2-"S"_{"c"}^2)/(2*"S"_{"a"}*"S"_{"b"})`

Example

`"-0.371429"=(("10m")^2+("14m")^2-("20m")^2)/(2*"10m"*"14m")`

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Cos C given Three Sides of Triangle Solution

STEP 0: Pre-Calculation Summary

Formula Used

Cos C = (Side A of Triangle^2+Side B of Triangle^2-Side C of Triangle^2)/(2*Side A of Triangle*Side B of Triangle)
cos C = (S_a^2+S_b^2-S_c^2)/(2*S_a*S_b)
This formula uses 4 Variables

Variables Used

Cos C - Cos C is the value of the trigonometric cosine function of the angle C of the triangle.
Side A of Triangle - (Measured in Meter) - The Side A of Triangle is the length of the side A, of the three sides of the triangle. In other words, the side A of the Triangle is the side opposite to the angle A.
Side B of Triangle - (Measured in Meter) - The Side B of Triangle is the length of the side B of the three sides. In other words, the side Bof the Triangle is the side opposite to the angle B.
Side C of Triangle - (Measured in Meter) - The Side C of Triangle is the length of the side C of the three sides. In other words, side C of the Triangle is the side opposite to angle C.

STEP 1: Convert Input(s) to Base Unit

Side A of Triangle: 10 Meter --> 10 Meter No Conversion Required
Side B of Triangle: 14 Meter --> 14 Meter No Conversion Required
Side C of Triangle: 20 Meter --> 20 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

cos C = (S_a^2+S_b^2-S_c^2)/(2*S_a*S_b) --> (10^2+14^2-20^2)/(2*10*14)

Evaluating ... ...

cos C = -0.371428571428571

STEP 3: Convert Result to Output's Unit

-0.371428571428571 --> No Conversion Required

FINAL ANSWER

-0.371428571428571 ≈ -0.371429 <-- Cos C

(Calculation completed in 00.020 seconds)

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< 3 Cosine Formula or Cosine Rule Calculators

Cos A given Three Sides of Triangle

Go Cos A = (Side B of Triangle^2+Side C of Triangle^2-Side A of Triangle^2)/(2*Side B of Triangle*Side C of Triangle)

Cos B given Three Sides of Triangle

Go Cos B = (Side C of Triangle^2+Side A of Triangle^2-Side B of Triangle^2)/(2*Side A of Triangle*Side C of Triangle)

Cos C given Three Sides of Triangle

Go Cos C = (Side A of Triangle^2+Side B of Triangle^2-Side C of Triangle^2)/(2*Side A of Triangle*Side B of Triangle)

Cos C given Three Sides of Triangle Formula

Cos C = (Side A of Triangle^2+Side B of Triangle^2-Side C of Triangle^2)/(2*Side A of Triangle*Side B of Triangle)
cos C = (S_a^2+S_b^2-S_c^2)/(2*S_a*S_b)

What is a Triangle?

The Triangle is the type of polygon, which have three sides and three vertices. This is a two-dimensional figure with three straight sides. A triangle is considered a 3-sided polygon. The sum of all the three angles of a triangle is equal to 180°. The triangle is contained in a single plane. Based on its sides and angle measurement, the triangle has six types.

What is Cosine Function in a Triangle?

The Cosine Function (or cos function) in a triangle is the ratio of the adjacent side to that of the hypotenuse.

How to Calculate Cos C given Three Sides of Triangle?

Cos C given Three Sides of Triangle calculator uses Cos C = (Side A of Triangle^2+Side B of Triangle^2-Side C of Triangle^2)/(2*Side A of Triangle*Side B of Triangle) to calculate the Cos C, The Cos C given Three Sides of Triangle formula is defined as the value of cos C using the values of the three sides of the triangle. Cos C is denoted by cos C symbol.

How to calculate Cos C given Three Sides of Triangle using this online calculator? To use this online calculator for Cos C given Three Sides of Triangle, enter Side A of Triangle (S_a), Side B of Triangle (S_b) & Side C of Triangle (S_c) and hit the calculate button. Here is how the Cos C given Three Sides of Triangle calculation can be explained with given input values -> -0.371429 = (10^2+14^2-20^2)/(2*10*14).

FAQ

What is Cos C given Three Sides of Triangle?

The Cos C given Three Sides of Triangle formula is defined as the value of cos C using the values of the three sides of the triangle and is represented as cos C = (S_a^2+S_b^2-S_c^2)/(2*S_a*S_b) or Cos C = (Side A of Triangle^2+Side B of Triangle^2-Side C of Triangle^2)/(2*Side A of Triangle*Side B of Triangle). The Side A of Triangle is the length of the side A, of the three sides of the triangle. In other words, the side A of the Triangle is the side opposite to the angle A, The Side B of Triangle is the length of the side B of the three sides. In other words, the side Bof the Triangle is the side opposite to the angle B & The Side C of Triangle is the length of the side C of the three sides. In other words, side C of the Triangle is the side opposite to angle C.

How to calculate Cos C given Three Sides of Triangle?

The Cos C given Three Sides of Triangle formula is defined as the value of cos C using the values of the three sides of the triangle is calculated using Cos C = (Side A of Triangle^2+Side B of Triangle^2-Side C of Triangle^2)/(2*Side A of Triangle*Side B of Triangle). To calculate Cos C given Three Sides of Triangle, you need Side A of Triangle (S_a), Side B of Triangle (S_b) & Side C of Triangle (S_c). With our tool, you need to enter the respective value for Side A of Triangle, Side B of Triangle & Side C of Triangle and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

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