Angle B of Triangle Calculator

✖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%
✖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%

✖Angle B of Triangle is the measure of the wideness of two sides that join to form the corner, opposite to side B of the Triangle.ⓘ Angle B of Triangle [∠B]

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Formula

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Angle B of Triangle

Formula

`"∠B" = acos(("S"_{"c"}^2+"S"_{"a"}^2-"S"_{"b"}^2)/(2*"S"_{"c"}*"S"_{"a"}))`

Example

`"40.5358°"=acos((("20m")^2+("10m")^2-("14m")^2)/(2*"20m"*"10m"))`

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Download Important Formulas of Triangle Formulas PDF

Angle B of Triangle Solution

STEP 0: Pre-Calculation Summary

Formula Used

Angle B of Triangle = acos((Side C of Triangle^2+Side A of Triangle^2-Side B of Triangle^2)/(2*Side C of Triangle*Side A of Triangle))
∠B = acos((S_c^2+S_a^2-S_b^2)/(2*S_c*S_a))
This formula uses 2 Functions, 4 Variables

Functions Used

cos - Cosine of an angle is the ratio of the side adjacent to the angle to the hypotenuse of the triangle., cos(Angle)
acos - The inverse cosine function, is the inverse function of the cosine function. It is the function that takes a ratio as an input and returns the angle whose cosine is equal to that ratio., acos(Number)

Variables Used

Angle B of Triangle - (Measured in Radian) - Angle B of Triangle is the measure of the wideness of two sides that join to form the corner, opposite to side B of the Triangle.
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.
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.

STEP 1: Convert Input(s) to Base Unit

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

STEP 2: Evaluate Formula

Substituting Input Values in Formula

∠B = acos((S_c^2+S_a^2-S_b^2)/(2*S_c*S_a)) --> acos((20^2+10^2-14^2)/(2*20*10))

Evaluating ... ...

∠B = 0.707483211779343

STEP 3: Convert Result to Output's Unit

0.707483211779343 Radian -->40.5358021113242 Degree (Check conversion here)

FINAL ANSWER

40.5358021113242 ≈ 40.5358 Degree <-- Angle B of Triangle

(Calculation completed in 00.004 seconds)

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Home » Math » Geometry » 2D Geometry » Triangle » Triangle » Important Formulas of Triangle » Angles of Triangle » Angle B of Triangle

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Created by Dhruv Walia

Indian Institute of Technology, Indian School of Mines, DHANBAD (IIT ISM), Dhanbad, Jharkhand

Dhruv Walia has created this Calculator and 1100+ more calculators!

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Mumbai University (DJSCE), Mumbai

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< 4 Angles of Triangle Calculators

Angle A of Triangle

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

Angle B of Triangle

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

Angle C of Triangle

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

Third Angle of Triangle given Two Angles

Go Angle C of Triangle = pi-(Angle A of Triangle+Angle B of Triangle)

< 4 Angle of Triangle Calculators

Angle A of Triangle

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

Angle B of Triangle

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

Angle C of Triangle

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

Third Angle of Triangle given Two Angles

Go Angle C of Triangle = pi-(Angle A of Triangle+Angle B of Triangle)

Angle B of Triangle Formula

Angle B of Triangle = acos((Side C of Triangle^2+Side A of Triangle^2-Side B of Triangle^2)/(2*Side C of Triangle*Side A of Triangle))
∠B = acos((S_c^2+S_a^2-S_b^2)/(2*S_c*S_a))

What is 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 the angle of Triangle is calculated?

A Triangle with three sides has three angles formed between the intersection of the sides. The sum of all the angles of any triangle ( like an isosceles, scalene, and equilateral ) is 180 degrees. When two angles of a triangle are given the third angle can be calculated by adding two angles and then subtracting the sum from 180 degrees.

How to Calculate Angle B of Triangle?

Angle B of Triangle calculator uses Angle B of Triangle = acos((Side C of Triangle^2+Side A of Triangle^2-Side B of Triangle^2)/(2*Side C of Triangle*Side A of Triangle)) to calculate the Angle B of Triangle, The Angle B of Triangle formula is defined as the measure of the wideness of two sides that join to form the corner, opposite to side B of the Triangle. Angle B of Triangle is denoted by ∠B symbol.

How to calculate Angle B of Triangle using this online calculator? To use this online calculator for Angle B 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. Here is how the Angle B of Triangle calculation can be explained with given input values -> 2322.53 = acos((20^2+10^2-14^2)/(2*20*10)).

FAQ

What is Angle B of Triangle?

The Angle B of Triangle formula is defined as the measure of the wideness of two sides that join to form the corner, opposite to side B of the Triangle and is represented as ∠B = acos((S_c^2+S_a^2-S_b^2)/(2*S_c*S_a)) or Angle B of Triangle = acos((Side C of Triangle^2+Side A of Triangle^2-Side B of Triangle^2)/(2*Side C of Triangle*Side A 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, 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.

How to calculate Angle B of Triangle?

The Angle B of Triangle formula is defined as the measure of the wideness of two sides that join to form the corner, opposite to side B of the Triangle is calculated using Angle B of Triangle = acos((Side C of Triangle^2+Side A of Triangle^2-Side B of Triangle^2)/(2*Side C of Triangle*Side A of Triangle)). To calculate Angle B of Triangle, you need Side C of Triangle (S_c), Side A of Triangle (S_a) & Side B of Triangle (S_b). With our tool, you need to enter the respective value for Side C of Triangle, Side A of Triangle & Side B 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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