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Side A of Triangle Formula

GoSide A of Triangle given Two Angles and Side B Formula

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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. Check FAQs

S a = \sqrt{{S b}^{2} + {S c}^{2} - 2 \cdot S b \cdot S c \cdot \cos (∠A)}

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

Side A of Triangle Example

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Here is how the Side A of Triangle equation looks like with Values.

Here is how the Side A of Triangle equation looks like with Units.

Here is how the Side A of Triangle equation looks like.

10.5369 = \sqrt{14^{2} + 20^{2} - 2 \cdot 14 \cdot 20 \cdot \cos (30)}

10.5369m = \sqrt{{14m}^{2} + {20m}^{2} - 2 \cdot 14m \cdot 20m \cdot \cos (30°)}

10.5369 = \sqrt{14^{2} + 20^{2} - 2 \cdot 14 \cdot 20 \cdot \cos (30)}

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Side A of Triangle Solution

Follow our step by step solution on how to calculate Side A of Triangle?

FIRST Step Consider the formula

S a = \sqrt{{S b}^{2} + {S c}^{2} - 2 \cdot S b \cdot S c \cdot \cos (∠A)}

Next Step Substitute values of Variables

∴

S a = \sqrt{{14m}^{2} + {20m}^{2} - 2 \cdot 14m \cdot 20m \cdot \cos (30°)}

Next Step Convert Units

∴

S a = \sqrt{{14m}^{2} + {20m}^{2} - 2 \cdot 14m \cdot 20m \cdot \cos (0.5236rad)}

Next Step Prepare to Evaluate

∴

S a = \sqrt{14^{2} + 20^{2} - 2 \cdot 14 \cdot 20 \cdot \cos (0.5236)}

Next Step Evaluate

∴

S a = 10.5368768561047m

LAST Step Rounding Answer

∴

S a = 10.5369m

Side A of Triangle Formula Elements

Variables

Functions

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 B 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.

Symbol: S_b

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Side B 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 A of Triangle

Angle A of Triangle is the measure of the wideness of two sides that join to form the corner, opposite to the side A of the Triangle.

Symbol: ∠A

Measurement: AngleUnit: °

Note: Value should be greater than 0.

Formulas to find Angle A of Triangle

cos

Cosine of an angle is the ratio of the side adjacent to the angle to the hypotenuse of the triangle.

Syntax: cos(Angle)

sqrt

A square root function is a function that takes a non-negative number as an input and returns the square root of the given input number.

Syntax: sqrt(Number)

Other Formulas to find Side A of Triangle

Go Side A of Triangle given Two Angles and Side B

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

Other formulas in Side of Triangle category

Go Side B of Triangle

S b = \sqrt{{S a}^{2} + {S c}^{2} - 2 \cdot S a \cdot S c \cdot \cos (∠B)}

Go Side C of Triangle

S c = \sqrt{{S b}^{2} + {S a}^{2} - 2 \cdot S a \cdot S b \cdot \cos (∠C)}

How to Evaluate Side A of Triangle?

Side A of Triangle evaluator uses Side A of Triangle = sqrt(Side B of Triangle^2+Side C of Triangle^2-2*Side B of Triangle*Side C of Triangle*cos(Angle A of Triangle)) to evaluate the Side A of Triangle, Side A of Triangle is one of the three sides of the Triangle, calculated using the other two sides and angle A. Side A of Triangle is denoted by S_a symbol.

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

FAQs on Side A of Triangle

What is the formula to find Side A of Triangle?

The formula of Side A of Triangle is expressed as Side A of Triangle = sqrt(Side B of Triangle^2+Side C of Triangle^2-2*Side B of Triangle*Side C of Triangle*cos(Angle A of Triangle)). Here is an example- 10.53688 = sqrt(14^2+20^2-2*14*20*cos(0.5235987755982)).

How to calculate Side A of Triangle?

With Side B of Triangle (S_b), Side C of Triangle (S_c) & Angle A of Triangle (∠A) we can find Side A of Triangle using the formula - Side A of Triangle = sqrt(Side B of Triangle^2+Side C of Triangle^2-2*Side B of Triangle*Side C of Triangle*cos(Angle A of Triangle)). This formula also uses Cosine (cos), Square Root (sqrt) function(s).

What are the other ways to Calculate Side A of Triangle?

Here are the different ways to Calculate Side A of Triangle-

Side A of Triangle=Side B of Triangle*sin(Angle A of Triangle)/sin(Angle B of Triangle)

Can the Side A of Triangle be negative?

No, the Side A of Triangle, measured in Length cannot be negative.

Which unit is used to measure Side A of Triangle?

Side A of Triangle is usually measured using the Meter[m] for Length. Millimeter[m], Kilometer[m], Decimeter[m] are the few other units in which Side A of Triangle can be measured.

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Side A of Triangle Formula

​GoSide A of Triangle given Two Angles and Side B Formula

Side A of Triangle Example

Side A of Triangle Solution

Side A of Triangle Formula Elements

Other Formulas to find Side A of Triangle

Other formulas in Side of Triangle category

How to Evaluate Side A of Triangle?

FAQs on Side A of Triangle

Variable Name

GoSide A of Triangle given Two Angles and Side B Formula