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Angle A of Triangle Formula

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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. Check FAQs

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

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

Angle A of Triangle Example

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

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

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

27.6604 = a \cos (\frac{20^{2} + 14^{2} - 10^{2}}{2 \cdot 20 \cdot 14})

27.6604° = a \cos (\frac{{20m}^{2} + {14m}^{2} - {10m}^{2}}{2 \cdot 20m \cdot 14m})

27.6604 = a \cos (\frac{20^{2} + 14^{2} - 10^{2}}{2 \cdot 20 \cdot 14})

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Angle A of Triangle Solution

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

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

∠A = a \cos (\frac{{20m}^{2} + {14m}^{2} - {10m}^{2}}{2 \cdot 20m \cdot 14m})

Next Step Prepare to Evaluate

∴

∠A = a \cos (\frac{20^{2} + 14^{2} - 10^{2}}{2 \cdot 20 \cdot 14})

Next Step Evaluate

∴

∠A = 0.482765923325734rad

Next Step Convert to Output's Unit

∴

∠A = 27.6604498993061°

LAST Step Rounding Answer

∴

∠A = 27.6604°

Angle A of Triangle Formula Elements

Variables

Functions

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

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

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 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

cos

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

Syntax: cos(Angle)

acos

The inverse cosine function, is the inverse function of the cosine function. It is the function that takes a ratio as an input and returns the angle whose cosine is equal to that ratio.

Syntax: acos(Number)

Other formulas in Angles of Triangle category

Go Third Angle of Triangle given Two Angles

∠C = π - (∠A + ∠B)

Go Angle B of Triangle

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

Go Angle C of Triangle

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

How to Evaluate Angle A of Triangle?

Angle A of Triangle evaluator uses Angle A of Triangle = acos((Side C of Triangle^2+Side B of Triangle^2-Side A of Triangle^2)/(2*Side C of Triangle*Side B of Triangle)) to evaluate the Angle A of Triangle, The Angle A of Triangle formula is defined as the measure of the wideness of two sides that join to form the corner, opposite to side A of the Triangle. Angle A of Triangle is denoted by ∠A symbol.

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

FAQs on Angle A of Triangle

What is the formula to find Angle A of Triangle?

The formula of Angle A of Triangle is expressed as Angle A of Triangle = acos((Side C of Triangle^2+Side B of Triangle^2-Side A of Triangle^2)/(2*Side C of Triangle*Side B of Triangle)). Here is an example- 1584.827 = acos((20^2+14^2-10^2)/(2*20*14)).

How to calculate Angle A of Triangle?

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

Can the Angle A of Triangle be negative?

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

Which unit is used to measure Angle A of Triangle?

Angle A of Triangle is usually measured using the Degree[°] for Angle. Radian[°], Minute[°], Second[°] are the few other units in which Angle A of Triangle can be measured.

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Angle A of Triangle Formula

Angle A of Triangle Example

Angle A of Triangle Solution

Angle A of Triangle Formula Elements

Other formulas in Angles of Triangle category

How to Evaluate Angle A of Triangle?

FAQs on Angle A of Triangle

Variable Name