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

GoArea of Triangle by Heron's Formula Formula

GoArea of Triangle given Base and Height Formula

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The Area of Triangle is the amount of region or space occupied by the Triangle. Check FAQs

A = \frac{S a \cdot S c}{2} \cdot (\sin (∠B))

A - Area of Triangle?S_a - Side A of Triangle?S_c - Side C of Triangle?∠B - Angle B of Triangle?

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

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Here is how the Area of Triangle given Sides A and C and Sine of Angle B equation looks like with Values.

Here is how the Area of Triangle given Sides A and C and Sine of Angle B equation looks like with Units.

Here is how the Area of Triangle given Sides A and C and Sine of Angle B equation looks like.

64.2788 = \frac{10 \cdot 20}{2} \cdot (\sin (40))

64.2788m² = \frac{10m \cdot 20m}{2} \cdot (\sin (40°))

64.2788 = \frac{10 \cdot 20}{2} \cdot (\sin (40))

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

Follow our step by step solution on how to calculate Area of Triangle given Sides A and C and Sine of Angle B?

FIRST Step Consider the formula

A = \frac{S a \cdot S c}{2} \cdot (\sin (∠B))

Next Step Substitute values of Variables

∴

A = \frac{10m \cdot 20m}{2} \cdot (\sin (40°))

Next Step Convert Units

∴

A = \frac{10m \cdot 20m}{2} \cdot (\sin (0.6981rad))

Next Step Prepare to Evaluate

∴

A = \frac{10 \cdot 20}{2} \cdot (\sin (0.6981))

Next Step Evaluate

∴

A = 64.2787609686439m²

LAST Step Rounding Answer

∴

A = 64.2788m²

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

Variables

Functions

Area of Triangle

The Area of Triangle is the amount of region or space occupied by the Triangle.

Symbol: A

Measurement: AreaUnit: m²

Note: Value should be greater than 0.

Formulas to find Area of Triangle

Side A 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.

Symbol: S_a

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Side A of Triangle

Side C 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.

Symbol: S_c

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Side C of Triangle

Angle B of Triangle

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.

Symbol: ∠B

Measurement: AngleUnit: °

Note: Value should be between 0 to 180.

Formulas to find Angle B of Triangle

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.

Syntax: sin(Angle)

Credits

Created by Surjojoti Som

Rashtreeya Vidyalaya College of Engineering (RVCE), Bangalore

Surjojoti Som has created this Formula and 200+ more formulas!

Verified by Nayana Phulphagar

Institute of Chartered and Financial Analysts of India National college (ICFAI National College), HUBLI

Nayana Phulphagar has verified this Formula and 1500+ more formulas!

Other Formulas to find Area of Triangle

Go Area of Triangle by Heron's Formula

A = \sqrt{s \cdot (s - S a) \cdot (s - S b) \cdot (s - S c)}

Go Area of Triangle given Base and Height

A = \frac{1}{2} \cdot S c \cdot h c

Go Area of Triangle

A = \frac{\sqrt{(S a + S b + S c) \cdot (S b + S c - S a) \cdot (S a - S b + S c) \cdot (S a + S b - S c)}}{4}

Go Area of Triangle given Two Angles and Third Side

A = \frac{{S a}^{2} \cdot \sin (∠B) \cdot \sin (∠C)}{2 \cdot \sin (π - ∠B - ∠C)}

How to Evaluate Area of Triangle given Sides A and C and Sine of Angle B?

Area of Triangle given Sides A and C and Sine of Angle B evaluator uses Area of Triangle = (Side A of Triangle*Side C of Triangle)/2*(sin(Angle B of Triangle)) to evaluate the Area of Triangle, The Area of Triangle given Sides A and C and Sine of Angle B formula is defined as as the region occupied inside the triangle, calculated using its two sides A & C and Sin of Angle B. Area of Triangle is denoted by A symbol.

How to evaluate Area of Triangle given Sides A and C and Sine of Angle B using this online evaluator? To use this online evaluator for Area of Triangle given Sides A and C and Sine of Angle B, enter Side A of Triangle (S_a), Side C of Triangle (S_c) & Angle B of Triangle (∠B) and hit the calculate button.

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

What is the formula to find Area of Triangle given Sides A and C and Sine of Angle B?

The formula of Area of Triangle given Sides A and C and Sine of Angle B is expressed as Area of Triangle = (Side A of Triangle*Side C of Triangle)/2*(sin(Angle B of Triangle)). Here is an example- 64.27876 = (10*20)/2*(sin(0.698131700797601)).

How to calculate Area of Triangle given Sides A and C and Sine of Angle B?

With Side A of Triangle (S_a), Side C of Triangle (S_c) & Angle B of Triangle (∠B) we can find Area of Triangle given Sides A and C and Sine of Angle B using the formula - Area of Triangle = (Side A of Triangle*Side C of Triangle)/2*(sin(Angle B of Triangle)). This formula also uses Sine (sin) function(s).

What are the other ways to Calculate Area of Triangle?

Here are the different ways to Calculate Area 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
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

Can the Area of Triangle given Sides A and C and Sine of Angle B be negative?

No, the Area of Triangle given Sides A and C and Sine of Angle B, measured in Area cannot be negative.

Which unit is used to measure Area of Triangle given Sides A and C and Sine of Angle B?

Area of Triangle given Sides A and C and Sine of Angle B is usually measured using the Square Meter[m²] for Area. Square Kilometer[m²], Square Centimeter[m²], Square Millimeter[m²] are the few other units in which Area of Triangle given Sides A and C and Sine of Angle B can be measured.

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

​GoArea of Triangle by Heron's Formula Formula

​GoArea of Triangle given Base and Height Formula

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

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

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

Credits

Other Formulas to find Area of Triangle

How to Evaluate Area of Triangle given Sides A and C and Sine of Angle B?

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

Variable Name

GoArea of Triangle by Heron's Formula Formula

GoArea of Triangle given Base and Height Formula