Angle C of Triangle Calculator

✖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 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%

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

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Formula

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Angle C of Triangle

Formula

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

Example

`"111.8037°"=acos((("14m")^2+("10m")^2-("20m")^2)/(2*"14m"*"10m"))`

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Angle C of Triangle Solution

STEP 0: Pre-Calculation Summary

Formula Used

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))
∠C = acos((S_b^2+S_a^2-S_c^2)/(2*S_b*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 C of Triangle - (Measured in Radian) - Angle C of Triangle is the measure of the wideness of two sides that join to form the corner, opposite to side C of the Triangle.
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 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

Side B of Triangle: 14 Meter --> 14 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

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

Evaluating ... ...

∠C = 1.95134351848472

STEP 3: Convert Result to Output's Unit

1.95134351848472 Radian -->111.803747989404 Degree (Check conversion here)

FINAL ANSWER

111.803747989404 ≈ 111.8037 Degree <-- Angle C of Triangle

(Calculation completed in 00.020 seconds)

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

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Created by Dhruv Walia

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

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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 C of Triangle Formula

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))
∠C = acos((S_b^2+S_a^2-S_c^2)/(2*S_b*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 C of Triangle?

Angle C of Triangle calculator uses 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)) to calculate the Angle C of Triangle, The Angle C of Triangle formula is defined as the measure of the wideness of two sides that join to form the corner, opposite to side C of the Triangle. Angle C of Triangle is denoted by ∠C symbol.

How to calculate Angle C of Triangle using this online calculator? To use this online calculator for Angle C of Triangle, enter Side B of Triangle (S_b), Side A of Triangle (S_a) & Side C of Triangle (S_c) and hit the calculate button. Here is how the Angle C of Triangle calculation can be explained with given input values -> 6405.883 = acos((14^2+10^2-20^2)/(2*14*10)).

FAQ

What is Angle C of Triangle?

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

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

How many ways are there to calculate Angle C of Triangle?

In this formula, Angle C of Triangle uses Side B of Triangle, Side A of Triangle & Side C of Triangle. We can use 2 other way(s) to calculate the same, which is/are as follows -

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

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