Area of Triangle given Two Angles and Third Side 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%
✖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]			+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]			+10% -10%

✖The Area of Triangle is the amount of region or space occupied by the Triangle.ⓘ Area of Triangle given Two Angles and Third Side [A]

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Area of Triangle given Two Angles and Third Side Solution

STEP 0: Pre-Calculation Summary

Formula Used

Area of Triangle = (Side A of Triangle^2*sin(Angle B of Triangle)*sin(Angle C of Triangle))/(2*sin(pi-Angle B of Triangle-Angle C of Triangle))
A = (S_a^2*sin(∠B)*sin(∠C))/(2*sin(pi-∠B-∠C))
This formula uses 1 Constants, 1 Functions, 4 Variables

Constants Used

pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288

Functions Used

sin - Sine is a trigonometric function that describes the ratio of the length of the opposite side of a right triangle to the length of the hypotenuse., sin(Angle)

Variables Used

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.
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.
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.

STEP 1: Convert Input(s) to Base Unit

Side A of Triangle: 10 Meter --> 10 Meter No Conversion Required
Angle B of Triangle: 40 Degree --> 0.698131700797601 Radian (Check conversion here)
Angle C of Triangle: 110 Degree --> 1.9198621771934 Radian (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

A = (S_a^2*sin(∠B)*sin(∠C))/(2*sin(pi-∠B-∠C)) --> (10^2*sin(0.698131700797601)*sin(1.9198621771934))/(2*sin(pi-0.698131700797601-1.9198621771934))

Evaluating ... ...

A = 60.4022773554523

STEP 3: Convert Result to Output's Unit

60.4022773554523 Square Meter --> No Conversion Required

FINAL ANSWER

60.4022773554523 ≈ 60.40228 Square Meter <-- Area of Triangle

(Calculation completed in 00.007 seconds)

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Created by Venkata Sai Prasanna Aradhyula

Birla Institute of Technology & Science (BITS), Hyderabad

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< Area of Triangle Calculators

Area of Triangle

LaTeX Go Area of Triangle = sqrt((Side A of Triangle+Side B of Triangle+Side C of Triangle)*(Side B of Triangle+Side C of Triangle-Side A of Triangle)*(Side A of Triangle-Side B of Triangle+Side C of Triangle)*(Side A of Triangle+Side B of Triangle-Side C of Triangle))/4

Area of Triangle by Heron's Formula

LaTeX Go Area of Triangle = sqrt(Semiperimeter of Triangle*(Semiperimeter of Triangle-Side A of Triangle)*(Semiperimeter of Triangle-Side B of Triangle)*(Semiperimeter of Triangle-Side C of Triangle))

Area of Triangle given Two Angles and Third Side

LaTeX Go Area of Triangle = (Side A of Triangle^2*sin(Angle B of Triangle)*sin(Angle C of Triangle))/(2*sin(pi-Angle B of Triangle-Angle C of Triangle))

Area of Triangle given Base and Height

LaTeX Go Area of Triangle = 1/2*Side C of Triangle*Height on Side C of Triangle

< Area of Triangle Calculators

Area of Triangle

Area of Triangle given Two Angles and Third Side

LaTeX Go Area of Triangle = (Side A of Triangle^2*sin(Angle B of Triangle)*sin(Angle C of Triangle))/(2*sin(pi-Angle B of Triangle-Angle C of Triangle))

Area of Triangle given Two Sides and Third Angle

LaTeX Go Area of Triangle = Side A of Triangle*Side B of Triangle*sin(Angle C of Triangle)/2

Area of Triangle given Inradius and Semiperimeter

LaTeX Go Area of Triangle = Inradius of Triangle*Semiperimeter of Triangle

Area of Triangle given Two Angles and Third Side Formula

LaTeX Go

Area of Triangle = (Side A of Triangle^2*sin(Angle B of Triangle)*sin(Angle C of Triangle))/(2*sin(pi-Angle B of Triangle-Angle C of Triangle))
A = (S_a^2*sin(∠B)*sin(∠C))/(2*sin(pi-∠B-∠C))

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 Area of Triangle given Two Angles and Third Side?

Area of Triangle given Two Angles and Third Side calculator uses Area of Triangle = (Side A of Triangle^2*sin(Angle B of Triangle)*sin(Angle C of Triangle))/(2*sin(pi-Angle B of Triangle-Angle C of Triangle)) to calculate the Area of Triangle, The Area of Triangle given Two Angles and Third Side is defined as the total region that is enclosed by the three sides of any particular triangle, calculated using its one side and two angles. Area of Triangle is denoted by A symbol.

How to calculate Area of Triangle given Two Angles and Third Side using this online calculator? To use this online calculator for Area of Triangle given Two Angles and Third Side, enter Side A of Triangle (S_a), Angle B of Triangle (∠B) & Angle C of Triangle (∠C) and hit the calculate button. Here is how the Area of Triangle given Two Angles and Third Side calculation can be explained with given input values -> 60.40228 = (10^2*sin(0.698131700797601)*sin(1.9198621771934))/(2*sin(pi-0.698131700797601-1.9198621771934)).

FAQ

What is Area of Triangle given Two Angles and Third Side?

The Area of Triangle given Two Angles and Third Side is defined as the total region that is enclosed by the three sides of any particular triangle, calculated using its one side and two angles and is represented as A = (S_a^2*sin(∠B)*sin(∠C))/(2*sin(pi-∠B-∠C)) or Area of Triangle = (Side A of Triangle^2*sin(Angle B of Triangle)*sin(Angle C of Triangle))/(2*sin(pi-Angle B of Triangle-Angle C 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, 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 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.

How to calculate Area of Triangle given Two Angles and Third Side?

The Area of Triangle given Two Angles and Third Side is defined as the total region that is enclosed by the three sides of any particular triangle, calculated using its one side and two angles is calculated using Area of Triangle = (Side A of Triangle^2*sin(Angle B of Triangle)*sin(Angle C of Triangle))/(2*sin(pi-Angle B of Triangle-Angle C of Triangle)). To calculate Area of Triangle given Two Angles and Third Side, you need Side A of Triangle (S_a), Angle B of Triangle (∠B) & Angle C of Triangle (∠C). With our tool, you need to enter the respective value for Side A of Triangle, Angle B of Triangle & Angle 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 Area of Triangle?

In this formula, Area of Triangle uses Side A of Triangle, Angle B of Triangle & Angle C of Triangle. We can use 3 other way(s) to calculate the same, which is/are as follows -

Area of Triangle = sqrt(Semiperimeter of Triangle*(Semiperimeter of Triangle-Side A of Triangle)*(Semiperimeter of Triangle-Side B of Triangle)*(Semiperimeter of Triangle-Side C of Triangle))
Area of Triangle = 1/2*Side C of Triangle*Height on Side C of Triangle
Area of Triangle = sqrt((Side A of Triangle+Side B of Triangle+Side C of Triangle)*(Side B of Triangle+Side C of Triangle-Side A of Triangle)*(Side A of Triangle-Side B of Triangle+Side C of Triangle)*(Side A of Triangle+Side B of Triangle-Side C of Triangle))/4

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