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Cos B given Three Sides of Triangle Formula

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Cos B is the value of the trigonometric cosine function of the angle B of the triangle. Check FAQs

cos ∠B = \frac{{S c}^{2} + {S a}^{2} - {S b}^{2}}{2 \cdot S a \cdot S c}

cos ∠B - Cos B?S_c - Side C of Triangle?S_a - Side A of Triangle?S_b - Side B of Triangle?

Cos B given Three Sides of Triangle Example

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Here is how the Cos B given Three Sides of Triangle equation looks like with Values.

Here is how the Cos B given Three Sides of Triangle equation looks like with Units.

Here is how the Cos B given Three Sides of Triangle equation looks like.

0.76 = \frac{20^{2} + 10^{2} - 14^{2}}{2 \cdot 10 \cdot 20}

0.76 = \frac{{20m}^{2} + {10m}^{2} - {14m}^{2}}{2 \cdot 10m \cdot 20m}

0.76 = \frac{20^{2} + 10^{2} - 14^{2}}{2 \cdot 10 \cdot 20}

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Cos B given Three Sides of Triangle Solution

Follow our step by step solution on how to calculate Cos B given Three Sides of Triangle?

FIRST Step Consider the formula

cos ∠B = \frac{{S c}^{2} + {S a}^{2} - {S b}^{2}}{2 \cdot S a \cdot S c}

Next Step Substitute values of Variables

∴

cos ∠B = \frac{{20m}^{2} + {10m}^{2} - {14m}^{2}}{2 \cdot 10m \cdot 20m}

Next Step Prepare to Evaluate

∴

cos ∠B = \frac{20^{2} + 10^{2} - 14^{2}}{2 \cdot 10 \cdot 20}

LAST Step Evaluate

∴

cos ∠B = 0.76

Cos B given Three Sides of Triangle Formula Elements

Variables

Cos B

Cos B is the value of the trigonometric cosine function of the angle B of the triangle.

Symbol: cos ∠B

Measurement: NAUnit: Unitless

Note: Value should be between -1.01 to 1.01.

Formulas to find Cos B

Side C of Triangle

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.

Symbol: S_c

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Side C of Triangle

Side A 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.

Symbol: S_a

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Side A of Triangle

Side B of Triangle

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.

Symbol: S_b

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Side B of Triangle

Credits

Created by Surjojoti Som

Rashtreeya Vidyalaya College of Engineering (RVCE), Bangalore

Surjojoti Som has created this Formula and 200+ more formulas!

Verified by Nayana Phulphagar

Institute of Chartered and Financial Analysts of India National college (ICFAI National College), HUBLI

Nayana Phulphagar has verified this Formula and 1500+ more formulas!

Other formulas in Cosine Formula or Cosine Rule category

Go Cos A given Three Sides of Triangle

cos ∠A = \frac{{S b}^{2} + {S c}^{2} - {S a}^{2}}{2 \cdot S b \cdot S c}

Go Cos C given Three Sides of Triangle

cos ∠C = \frac{{S a}^{2} + {S b}^{2} - {S c}^{2}}{2 \cdot S a \cdot S b}

How to Evaluate Cos B given Three Sides of Triangle?

Cos B given Three Sides of Triangle evaluator uses 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) to evaluate the Cos B, The Cos B given Three Sides of Triangle formula is defined as the value of cos B using the values of the three sides of the triangle. Cos B is denoted by cos ∠B symbol.

How to evaluate Cos B given Three Sides of Triangle using this online evaluator? To use this online evaluator for Cos B given Three Sides of Triangle, enter Side C of Triangle (S_c), Side A of Triangle (S_a) & Side B of Triangle (S_b) and hit the calculate button.

FAQs on Cos B given Three Sides of Triangle

What is the formula to find Cos B given Three Sides of Triangle?

The formula of Cos B given Three Sides of Triangle is expressed as 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). Here is an example- 0.76 = (20^2+10^2-14^2)/(2*10*20).

How to calculate Cos B given Three Sides of Triangle?

With Side C of Triangle (S_c), Side A of Triangle (S_a) & Side B of Triangle (S_b) we can find Cos B given Three Sides of Triangle using the formula - 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).

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Cos B given Three Sides of Triangle Formula

Cos B given Three Sides of Triangle Example

Cos B given Three Sides of Triangle Solution

Cos B given Three Sides of Triangle Formula Elements

Credits

Other formulas in Cosine Formula or Cosine Rule category

How to Evaluate Cos B given Three Sides of Triangle?

FAQs on Cos B given Three Sides of Triangle

Variable Name