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

GoSide 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

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

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

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

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

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

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

9.7085 = \frac{14 - 20 \cdot \cos (30)}{\cos (110)}

9.7085m = \frac{14m - 20m \cdot \cos (30°)}{\cos (110°)}

9.7085 = \frac{14 - 20 \cdot \cos (30)}{\cos (110)}

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

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

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

S a = \frac{14m - 20m \cdot \cos (30°)}{\cos (110°)}

Next Step Convert Units

∴

S a = \frac{14m - 20m \cdot \cos (0.5236rad)}{\cos (1.9199rad)}

Next Step Prepare to Evaluate

∴

S a = \frac{14 - 20 \cdot \cos (0.5236)}{\cos (1.9199)}

Next Step Evaluate

∴

S a = 9.70851612248557m

LAST Step Rounding Answer

∴

S a = 9.7085m

Side A of Triangle given Two Sides and Two Angles A 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

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

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

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 B and C

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

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)}

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 A and C?

Side A of Triangle given Two Sides and Two Angles A and C evaluator uses Side A of Triangle = (Side B of Triangle-Side C of Triangle*cos(Angle A of Triangle))/cos(Angle C of Triangle) to evaluate the Side A of Triangle, The Side A of Triangle given Two Sides and Two Angles A and C formula is defined as the length of side A using Angle A 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 A and C using this online evaluator? To use this online evaluator for Side A of Triangle given Two Sides and Two Angles A and C, enter Side B of Triangle (S_b), Side C of Triangle (S_c), Angle A of Triangle (∠A) & Angle C of Triangle (∠C) and hit the calculate button.

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

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

The formula of Side A of Triangle given Two Sides and Two Angles A and C is expressed as Side A of Triangle = (Side B of Triangle-Side C of Triangle*cos(Angle A of Triangle))/cos(Angle C of Triangle). Here is an example- 9.708516 = (14-20*cos(0.5235987755982))/cos(1.9198621771934).

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

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

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

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

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

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

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

​GoSide 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

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

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

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

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

Variable Name

GoSide 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