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Side A of Triangle given Two Sides and Two Angles B and C Formula

GoSide A of Triangle given Two Sides and Two Angles A and B Formula

GoSide A of Triangle given Two Sides and Two Angles A and C 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 = S b \cdot \cos (∠C) + S c \cdot \cos (∠B)

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

Side A of Triangle given Two Sides and Two Angles B and C Example

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Here is how the Side A of Triangle given Two Sides and Two Angles B and C equation looks like with Values.

Here is how the Side A of Triangle given Two Sides and Two Angles B and C equation looks like with Units.

Here is how the Side A of Triangle given Two Sides and Two Angles B and C equation looks like.

10.5326 = 14 \cdot \cos (110) + 20 \cdot \cos (40)

10.5326m = 14m \cdot \cos (110°) + 20m \cdot \cos (40°)

10.5326 = 14 \cdot \cos (110) + 20 \cdot \cos (40)

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Side A of Triangle given Two Sides and Two Angles B and C Solution

Follow our step by step solution on how to calculate Side A of Triangle given Two Sides and Two Angles B and C?

FIRST Step Consider the formula

S a = S b \cdot \cos (∠C) + S c \cdot \cos (∠B)

Next Step Substitute values of Variables

∴

S a = 14m \cdot \cos (110°) + 20m \cdot \cos (40°)

Next Step Convert Units

∴

S a = 14m \cdot \cos (1.9199rad) + 20m \cdot \cos (0.6981rad)

Next Step Prepare to Evaluate

∴

S a = 14 \cdot \cos (1.9199) + 20 \cdot \cos (0.6981)

Next Step Evaluate

∴

S a = 10.5326068558267m

LAST Step Rounding Answer

∴

S a = 10.5326m

Side A of Triangle given Two Sides and Two Angles B and C 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

Angle C of Triangle

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.

Symbol: ∠C

Measurement: AngleUnit: °

Note: Value should be between 0 to 180.

Formulas to find Angle C 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

cos

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

Syntax: cos(Angle)

Other Formulas to find Side A of Triangle

Go Side A of Triangle given Two Sides and Two Angles A and B

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

Go Side A of Triangle given Two Sides and Two Angles A and C

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

Other formulas in Projection Formulae in Triangles category

Go Side C of Triangle given Two Sides and Two Angles A and B

S c = S a \cdot \cos (∠B) + S b \cdot \cos (∠A)

Go Side B of Triangle given Two Sides and Two Angles A and C

S b = S a \cdot \cos (∠C) + S c \cdot \cos (∠A)

Go Side B of Triangle given Two Sides and Two Angles A and B

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

Go Side B of Triangle given Two Sides and Two Angles B and C

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

How to Evaluate Side A of Triangle given Two Sides and Two Angles B and C?

Side A of Triangle given Two Sides and Two Angles B and C evaluator uses Side A of Triangle = Side B of Triangle*cos(Angle C of Triangle)+Side C of Triangle*cos(Angle B of Triangle) to evaluate the Side A of Triangle, The Side A of Triangle given Two Sides and Two Angles B and C formula is defined as the length of side A using Angle B and C, and side B and C. Side A of Triangle is denoted by S_a symbol.

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

FAQs on Side A of Triangle given Two Sides and Two Angles B and C

What is the formula to find Side A of Triangle given Two Sides and Two Angles B and C?

The formula of Side A of Triangle given Two Sides and Two Angles B and C is expressed as Side A of Triangle = Side B of Triangle*cos(Angle C of Triangle)+Side C of Triangle*cos(Angle B of Triangle). Here is an example- 10.53261 = 14*cos(1.9198621771934)+20*cos(0.698131700797601).

How to calculate Side A of Triangle given Two Sides and Two Angles B and C?

With Side B of Triangle (S_b), Angle C of Triangle (∠C), Side C of Triangle (S_c) & Angle B of Triangle (∠B) we can find Side A of Triangle given Two Sides and Two Angles B and C using the formula - Side A of Triangle = Side B of Triangle*cos(Angle C of Triangle)+Side C of Triangle*cos(Angle B of Triangle). This formula also uses Cosine 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 C of Triangle-Side B of Triangle*cos(Angle A of Triangle))/cos(Angle B of Triangle)
Side A of Triangle=(Side B of Triangle-Side C of Triangle*cos(Angle A of Triangle))/cos(Angle C of Triangle)

Can the Side A of Triangle given Two Sides and Two Angles B and C be negative?

No, the Side A of Triangle given Two Sides and Two Angles B and C, measured in Length cannot be negative.

Which unit is used to measure Side A of Triangle given Two Sides and Two Angles B and C?

Side A of Triangle given Two Sides and Two Angles B and C 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 given Two Sides and Two Angles B and C can be measured.

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Side A of Triangle given Two Sides and Two Angles B and C Formula

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

​GoSide A of Triangle given Two Sides and Two Angles A and C Formula

Side A of Triangle given Two Sides and Two Angles B and C Example

Side A of Triangle given Two Sides and Two Angles B and C Solution

Side A of Triangle given Two Sides and Two Angles B and C Formula Elements

Other Formulas to find Side A of Triangle

Other formulas in Projection Formulae in Triangles category

How to Evaluate Side A of Triangle given Two Sides and Two Angles B and C?

FAQs on Side A of Triangle given Two Sides and Two Angles B and C

Variable Name

GoSide A of Triangle given Two Sides and Two Angles A and B Formula

GoSide A of Triangle given Two Sides and Two Angles A and C Formula