Area of Triangle given Side A and Sine of All Three Angles 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%
✖Sin B is the value of the trigonometric cosine function of the angle B of the triangle.ⓘ Sin B			+10% -10%
✖Sin C is the value of the trigonometric sine function of the angle C of the triangle.ⓘ Sin C			+10% -10%
✖Sin A is the value of the trigonometric sine function of the angle A of the triangle.ⓘ Sin A			+10% -10%

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

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Formula

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Area of Triangle given Side A and Sine of All Three Angles

Formula

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

Example

`"61.38776m²"=(("10m")^2*"0.64"*"0.94")/(2*"0.49")`

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Area of Triangle given Side A and Sine of All Three Angles Solution

STEP 0: Pre-Calculation Summary

Formula Used

Area of Triangle = (Side A of Triangle^2*Sin B*Sin C)/(2*Sin A)
A = (S_a^2*sin B*sin C)/(2*sin A)
This formula uses 5 Variables

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.
Sin B - Sin B is the value of the trigonometric cosine function of the angle B of the triangle.
Sin C - Sin C is the value of the trigonometric sine function of the angle C of the triangle.
Sin A - Sin A is the value of the trigonometric sine function of the angle A of the triangle.

STEP 1: Convert Input(s) to Base Unit

Side A of Triangle: 10 Meter --> 10 Meter No Conversion Required
Sin B: 0.64 --> No Conversion Required
Sin C: 0.94 --> No Conversion Required
Sin A: 0.49 --> No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

A = (S_a^2*sin B*sin C)/(2*sin A) --> (10^2*0.64*0.94)/(2*0.49)

Evaluating ... ...

A = 61.3877551020408

STEP 3: Convert Result to Output's Unit

61.3877551020408 Square Meter --> No Conversion Required

FINAL ANSWER

61.3877551020408 ≈ 61.38776 Square Meter <-- Area of Triangle

(Calculation completed in 00.006 seconds)

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Created by Surjojoti Som

Rashtreeya Vidyalaya College of Engineering (RVCE), Bangalore

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< 17 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 Side A and Sine of All Three Angles

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

Area of Triangle given Side B and Sine of All Three Angles

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

Area of Triangle given Side C and Sine of All Three Angles

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

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 Side A and Sine of All Three Angles Formula

Area of Triangle = (Side A of Triangle^2*Sin B*Sin C)/(2*Sin A)
A = (S_a^2*sin B*sin C)/(2*sin A)

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 Side A and Sine of All Three Angles?

Area of Triangle given Side A and Sine of All Three Angles calculator uses Area of Triangle = (Side A of Triangle^2*Sin B*Sin C)/(2*Sin A) to calculate the Area of Triangle, The Area of Triangle given Side A and Sine of All Three Angles formula is defined as the region occupied inside the triangle, calculated using it's side A and sin of all three angles. Area of Triangle is denoted by A symbol.

How to calculate Area of Triangle given Side A and Sine of All Three Angles using this online calculator? To use this online calculator for Area of Triangle given Side A and Sine of All Three Angles, enter Side A of Triangle (S_a), Sin B (sin B), Sin C (sin C) & Sin A (sin A) and hit the calculate button. Here is how the Area of Triangle given Side A and Sine of All Three Angles calculation can be explained with given input values -> 61.38776 = (10^2*0.64*0.94)/(2*0.49).

FAQ

What is Area of Triangle given Side A and Sine of All Three Angles?

The Area of Triangle given Side A and Sine of All Three Angles formula is defined as the region occupied inside the triangle, calculated using it's side A and sin of all three angles and is represented as A = (S_a^2*sin B*sin C)/(2*sin A) or Area of Triangle = (Side A of Triangle^2*Sin B*Sin C)/(2*Sin A). 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, Sin B is the value of the trigonometric cosine function of the angle B of the triangle, Sin C is the value of the trigonometric sine function of the angle C of the triangle & Sin A is the value of the trigonometric sine function of the angle A of the triangle.

How to calculate Area of Triangle given Side A and Sine of All Three Angles?

The Area of Triangle given Side A and Sine of All Three Angles formula is defined as the region occupied inside the triangle, calculated using it's side A and sin of all three angles is calculated using Area of Triangle = (Side A of Triangle^2*Sin B*Sin C)/(2*Sin A). To calculate Area of Triangle given Side A and Sine of All Three Angles, you need Side A of Triangle (S_a), Sin B (sin B), Sin C (sin C) & Sin A (sin A). With our tool, you need to enter the respective value for Side A of Triangle, Sin B, Sin C & Sin A 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, Sin B, Sin C & Sin A. We can use 19 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*sin(Angle C of Triangle)/2
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 B of Triangle^2*Sin A*Sin C)/(2*Sin B)
Area of Triangle = (Side C of Triangle^2*Sin A*Sin B)/(2*Sin C)
Area of Triangle = (Side A of Triangle^2*Cosec A)/(2*Cosec B*Cosec C)
Area of Triangle = (Side B of Triangle^2*Cosec B)/(2*Cosec A*Cosec C)
Area of Triangle = (Side C of Triangle^2*Cosec C)/(2*Cosec A*Cosec B)

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