Cos B using Area and Sides A and C of Triangle Calculator

✖The Area of Triangle is the amount of region or space occupied by the Triangle.ⓘ Area of Triangle [A]			+10% -10%
✖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 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 B is the value of the trigonometric cosine function of the angle B of the triangle.ⓘ Cos B using Area and Sides A and C of Triangle [cos ∠B]

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Formula

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Cos B using Area and Sides A and C of Triangle

Formula

`"cos ∠B" = sqrt(1-((2*"A")/("S"_{"a"}*"S"_{"c"}))^2)`

Example

`"0.759934"=sqrt(1-((2*"65m²")/("10m"*"20m"))^2)`

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Cos B using Area and Sides A and C of Triangle Solution

STEP 0: Pre-Calculation Summary

Formula Used

Cos B = sqrt(1-((2*Area of Triangle)/(Side A of Triangle*Side C of Triangle))^2)
cos ∠B = sqrt(1-((2*A)/(S_a*S_c))^2)
This formula uses 1 Functions, 4 Variables

Functions Used

sqrt - A square root function is a function that takes a non-negative number as an input and returns the square root of the given input number., sqrt(Number)

Variables Used

Cos B - Cos B is the value of the trigonometric cosine function of the angle B of the triangle.
Area of Triangle - (Measured in Square Meter) - The Area of Triangle is the amount of region or space occupied by 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 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

Area of Triangle: 65 Square Meter --> 65 Square Meter No Conversion Required
Side A of Triangle: 10 Meter --> 10 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 ∠B = sqrt(1-((2*A)/(S_a*S_c))^2) --> sqrt(1-((2*65)/(10*20))^2)

Evaluating ... ...

cos ∠B = 0.759934207678533

STEP 3: Convert Result to Output's Unit

0.759934207678533 --> No Conversion Required

FINAL ANSWER

0.759934207678533 ≈ 0.759934 <-- Cos B

(Calculation completed in 00.004 seconds)

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Home » Math » Geometry » 2D Geometry » Triangle » Trigonometric Ratios using Sides and Area of Triangle » Cos B using Area and Sides A and C of Triangle

Credits

Created by Surjojoti Som

Rashtreeya Vidyalaya College of Engineering (RVCE), Bangalore

Surjojoti Som has created this Calculator and 100+ more calculators!

Verified by Harsh Raj

Indian Institute of Technology, Kharagpur (IIT KGP), West Bengal

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< 18 Trigonometric Ratios using Sides and Area of Triangle Calculators

Tan C using Area and Sides A and B of Triangle

Go Tan C = -((2*Area of Triangle)/sqrt((Side A of Triangle*Side B of Triangle+2*Area of Triangle)*(Side A of Triangle*Side B of Triangle-2*Area of Triangle)))

Cot C using Area and Sides A and B of Triangle

Go Cot C = -(sqrt((Side A of Triangle*Side B of Triangle+2*Area of Triangle)*(Side A of Triangle*Side B of Triangle-2*Area of Triangle))/(2*Area of Triangle))

Tan A using Area and Sides B and C of Triangle

Go Tan A = (2*Area of Triangle)/sqrt((Side B of Triangle*Side C of Triangle+2*Area of Triangle)*(Side B of Triangle*Side C of Triangle-2*Area of Triangle))

Tan B using Area and Sides A and C of Triangle

Go Tan B = (2*Area of Triangle)/sqrt((Side A of Triangle*Side C of Triangle+2*Area of Triangle)*(Side A of Triangle*Side C of Triangle-2*Area of Triangle))

Cot A using Area and Sides B and C of Triangle

Go Cot A = sqrt((Side B of Triangle*Side C of Triangle+2*Area of Triangle)*(Side B of Triangle*Side C of Triangle-2*Area of Triangle))/(2*Area of Triangle)

Cot B using Area and Sides A and C of Triangle

Go Cot B = sqrt((Side A of Triangle*Side C of Triangle+2*Area of Triangle)*(Side A of Triangle*Side C of Triangle-2*Area of Triangle))/(2*Area of Triangle)

Sec C using Area and Sides A and B of Triangle

Go Sec C = -1/(sqrt(1-((2*Area of Triangle)/(Side A of Triangle*Side B of Triangle))^2))

Cos C using Area and Sides A and B of Triangle

Go Cos C = -(sqrt(1-((2*Area of Triangle)/(Side A of Triangle*Side B of Triangle))^2))

Sec A using Area and Sides B and C of Triangle

Go Sec A = 1/sqrt(1-((2*Area of Triangle)/(Side B of Triangle*Side C of Triangle))^2)

Sec B using Area and Sides A and C of Triangle

Go Sec B = 1/sqrt(1-((2*Area of Triangle)/(Side A of Triangle*Side C of Triangle))^2)

Cos A using Area and Sides B and C of Triangle

Go Cos A = sqrt(1-((2*Area of Triangle)/(Side B of Triangle*Side C of Triangle))^2)

Cos B using Area and Sides A and C of Triangle

Go Cos B = sqrt(1-((2*Area of Triangle)/(Side A of Triangle*Side C of Triangle))^2)

Cosec A using Area and Sides B and C of Triangle

Go Cosec A = (Side B of Triangle*Side C of Triangle)/(2*Area of Triangle)

Cosec B using Area and Sides A and C of Triangle

Go Cosec B = (Side A of Triangle*Side C of Triangle)/(2*Area of Triangle)

Cosec C using Area and Sides A and B of Triangle

Go Cosec C = (Side A of Triangle*Side B of Triangle)/(2*Area of Triangle)

Sin B using Area and Sides A and C of Triangle

Go Sin B = (2*Area of Triangle)/(Side A of Triangle*Side C of Triangle)

Sin A using Area and Sides B and C of Triangle

Go Sin A = (2*Area of Triangle)/(Side B of Triangle*Side C of Triangle)

Sin C using Area and Sides A and B of Triangle

Go Sin C = (2*Area of Triangle)/(Side A of Triangle*Side B of Triangle)

Cos B using Area and Sides A and C of Triangle Formula

Cos B = sqrt(1-((2*Area of Triangle)/(Side A of Triangle*Side C of Triangle))^2)
cos ∠B = sqrt(1-((2*A)/(S_a*S_c))^2)

What is a Triangle ?

A Triangle is a 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.

How to Calculate Cos B using Area and Sides A and C of Triangle?

Cos B using Area and Sides A and C of Triangle calculator uses Cos B = sqrt(1-((2*Area of Triangle)/(Side A of Triangle*Side C of Triangle))^2) to calculate the Cos B, The Cos B using Area and Sides A and C of Triangle formula is defined as value of cos B using area and the sides A and C of the triangle. Cos B is denoted by cos ∠B symbol.

How to calculate Cos B using Area and Sides A and C of Triangle using this online calculator? To use this online calculator for Cos B using Area and Sides A and C of Triangle, enter Area of Triangle (A), Side A of Triangle (S_a) & Side C of Triangle (S_c) and hit the calculate button. Here is how the Cos B using Area and Sides A and C of Triangle calculation can be explained with given input values -> 0.759934 = sqrt(1-((2*65)/(10*20))^2).

FAQ

What is Cos B using Area and Sides A and C of Triangle?

The Cos B using Area and Sides A and C of Triangle formula is defined as value of cos B using area and the sides A and C of the triangle and is represented as cos ∠B = sqrt(1-((2*A)/(S_a*S_c))^2) or Cos B = sqrt(1-((2*Area of Triangle)/(Side A of Triangle*Side C of Triangle))^2). The Area of Triangle is the amount of region or space occupied by the 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 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 B using Area and Sides A and C of Triangle?

The Cos B using Area and Sides A and C of Triangle formula is defined as value of cos B using area and the sides A and C of the triangle is calculated using Cos B = sqrt(1-((2*Area of Triangle)/(Side A of Triangle*Side C of Triangle))^2). To calculate Cos B using Area and Sides A and C of Triangle, you need Area of Triangle (A), Side A of Triangle (S_a) & Side C of Triangle (S_c). With our tool, you need to enter the respective value for Area of Triangle, Side A 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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