Area of Triangle given Two Sides and Third Angle 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%
✖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 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 Sides and Third Angle [A]

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Formula

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Area of Triangle given Two Sides and Third Angle

Formula

`"A" = "S"_{"a"}*"S"_{"b"}*sin("∠C")/2`

Example

`"65.77848m²"="10m"*"14m"*sin("110°")/2`

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Area of Triangle given Two Sides and Third Angle Solution

STEP 0: Pre-Calculation Summary

Formula Used

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

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.
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.
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
Side B of Triangle: 14 Meter --> 14 Meter No Conversion Required
Angle C of Triangle: 110 Degree --> 1.9198621771934 Radian (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

A = S_a*S_b*sin(∠C)/2 --> 10*14*sin(1.9198621771934)/2

Evaluating ... ...

A = 65.7784834550223

STEP 3: Convert Result to Output's Unit

65.7784834550223 Square Meter --> No Conversion Required

FINAL ANSWER

65.7784834550223 ≈ 65.77848 Square Meter <-- Area of Triangle

(Calculation completed in 00.004 seconds)

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Created by Venkata Sai Prasanna Aradhyula

Birla Institute of Technology & Science (BITS), Hyderabad

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< 14 Area of Triangle Calculators

Area of Triangle

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

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

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 Three Exradii and Inradius

Go Area of Triangle = sqrt(Exradius Opposite to ∠A of Triangle*Exradius Opposite to ∠B of Triangle*Exradius Opposite to ∠C of Triangle*Inradius of Triangle)

Area of Triangle given Circumradius and Sides

Go Area of Triangle = (Side A of Triangle*Side B of Triangle*Side C of Triangle)/(4*Circumradius of Triangle)

Area of Triangle using Sides A and B and Cosec of Angle C

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

Area of Triangle using Sides B and C and Cosec of Angle A

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

Area of Triangle using Sides A and C and Cosec of Angle B

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

Area of Triangle given Sides B and C and Sine of Angle A

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

Area of Triangle given Sides A and C and Sine of Angle B

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

Area of Triangle given Two Sides and Third Angle

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

Area of Triangle given Semiperimeter, One Side and its Exradius

Go Area of Triangle = Exradius Opposite to ∠A of Triangle*(Semiperimeter of Triangle-Side A of Triangle)

Area of Triangle given Base and Height

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

Area of Triangle given Inradius and Semiperimeter

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

< 6 Area of Triangle Calculators

Area of Triangle

Area of Triangle by Heron's Formula

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

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

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

Area of Triangle given Base and Height

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

Area of Triangle given Inradius and Semiperimeter

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

Area of Triangle given Two Sides and Third Angle Formula

Area of Triangle = Side A of Triangle*Side B of Triangle*sin(Angle C of Triangle)/2
A = S_a*S_b*sin(∠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 Area of Triangle given Two Sides and Third Angle?

Area of Triangle given Two Sides and Third Angle calculator uses Area of Triangle = Side A of Triangle*Side B of Triangle*sin(Angle C of Triangle)/2 to calculate the Area of Triangle, The Area of Triangle given Two Sides and Third Angle formula is defined as the region occupied inside the triangle, calculated using its two sides and one angle. Area of Triangle is denoted by A symbol.

How to calculate Area of Triangle given Two Sides and Third Angle using this online calculator? To use this online calculator for Area of Triangle given Two Sides and Third Angle, enter Side A of Triangle (S_a), Side B of Triangle (S_b) & Angle C of Triangle (∠C) and hit the calculate button. Here is how the Area of Triangle given Two Sides and Third Angle calculation can be explained with given input values -> 65.77848 = 10*14*sin(1.9198621771934)/2.

FAQ

What is Area of Triangle given Two Sides and Third Angle?

The Area of Triangle given Two Sides and Third Angle formula is defined as the region occupied inside the triangle, calculated using its two sides and one angle and is represented as A = S_a*S_b*sin(∠C)/2 or Area of Triangle = Side A of Triangle*Side B of Triangle*sin(Angle C of Triangle)/2. 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 & 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 Sides and Third Angle?

The Area of Triangle given Two Sides and Third Angle formula is defined as the region occupied inside the triangle, calculated using its two sides and one angle is calculated using Area of Triangle = Side A of Triangle*Side B of Triangle*sin(Angle C of Triangle)/2. To calculate Area of Triangle given Two Sides and Third Angle, you need Side A of Triangle (S_a), Side B of Triangle (S_b) & Angle C of Triangle (∠C). With our tool, you need to enter the respective value for Side A of Triangle, Side 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, Side B of Triangle & Angle C of Triangle. We can use 24 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
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 = (Side A of Triangle*Side B of Triangle*Side C of Triangle)/(4*Circumradius of Triangle)
Area of Triangle = Inradius of Triangle*Semiperimeter of Triangle
Area of Triangle = sqrt(Exradius Opposite to ∠A of Triangle*Exradius Opposite to ∠B of Triangle*Exradius Opposite to ∠C of Triangle*Inradius of Triangle)
Area of Triangle = Exradius Opposite to ∠A of Triangle*(Semiperimeter of Triangle-Side A of Triangle)
Area of Triangle = (Side B of Triangle*Side C of Triangle)/2*(sin(Angle A of Triangle))
Area of Triangle = (Side A of Triangle*Side C of Triangle)/2*(sin(Angle B of Triangle))
Area of Triangle = (Side A of Triangle*Side B of Triangle)/(2*cosec(Angle C of Triangle))
Area of Triangle = (Side A of Triangle*Side B of Triangle)/(2*cosec(Angle C of Triangle))
Area of Triangle = (Side A of Triangle*Side C of Triangle)/(2*cosec(Angle B of Triangle))
Area of Triangle = (Side A of Triangle^2*Sin B*Sin C)/(2*Sin A)
Area of Triangle = (Side B of Triangle^2*Sin B*Sin C)/(2*Sin A)
Area of Triangle = (Side C of Triangle^2*Sin B*Sin C)/(2*Sin A)
Area of Triangle = (Side A of Triangle^2*cosec(Angle A of Triangle))/(2*cosec(Angle B of Triangle)*cosec(Angle C of Triangle))
Area of Triangle = (Side B of Triangle^2*cosec(Angle B of Triangle))/(2*cosec(Angle A of Triangle)*cosec(Angle C of Triangle))
Area of Triangle = (Side C of Triangle^2*cosec(Angle C of Triangle))/(2*cosec(Angle A of Triangle)*cosec(Angle B 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
Area of Triangle = Inradius of Triangle*Semiperimeter of Triangle
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 = 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

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