Area : sq cm

Perimeter : cm

## Determine angle of triangle when 3 Sides are given

**Step:1**SSS Method:First use The Law of Cosines to calculate one of the angle### Formula:

**cos(A) = (b**^{2}+ c^{2}− a^{2}) / 2bc### Example:Three sides are 8,6,7

### cos(A) = (62 + 72 − 82) / (2×6×7)

### A = 75.5°

**Step 2:**Again use the Law of Cosines to calcluate the second angle**cos(B) = (c**^{2}+ a^{2}− b^{2})/2ca### Example:cos(B) = (72 + 82 − 62)/(2×7×8)

### B = 46.6°

**Step 3:**Add the First and second angle,then subtract from 180 to get Third Angle.**C = 180° − Angle A° − Angle B°**### C = 180° − 75.5° − 46.6°

### C = 57.9°

## Calculate Angle when 2 sides and 1 angle is given

**Step:1**SAS Method:First use The Law of Cosines to calculate third side.### Formula:

**a**^{2}= b^{2}+ c^{2}− 2bc cosA### Example:Two sides are 5,7 and Angle 49°

### a

^{2}= 52 + 72 − 2 × 5 × 7 × cos(49°)### a = √28.075

### a = 5.3

**Step 2:**Then use Law of Sines ,find the smaller of other two angles. to calcluate the second angle**sin B / b = sin A / a**### Example:sin B = (sin(49°) × 5) / 5.29

### B = sin-1(0.7122...)

### B = 45.4°

**Step 3:**Add the First and second angle,then subtract from 180 to get Third Angle.**C = 180° − Angle A° − Angle B°**### C = 180° − 49° − 45.4°

### C = 85.6°

## Calculate Sides when Angle is given

**Step:1**ASA Method:First Calculate the third angle.### Formula:

**Angle A+Angle B+Angle C=180°**### Example:Angle A and Angle B are 32° and 47° ,Third Side is 21

### 32+47+Angle C=180°

### Angle C=180-79

### Angle C=101°

**Step 2:**Then use Law of Sines ,find the smaller of other two angles. to calcluate the second angle**a/Sin A=b/Sin B=c/Sin C**### Example:a/Sin A=c/Sin C

### a(Sin 101)=21(Sin 32)

### a=11.34

**Step 3:**Repeat the Second step to get the Other side**a/Sin A=b/Sin B=c/Sin C**### b/Sin B=c/Sin C

### b(Sin 101)=21(Sin 47)

### b=15.65

## Right Angle Triangle

**Right angle triangle is that one of the angles of a triangle is right angle(90°)**### The square of the hypotenuse is equal to the sum of the square of the base and the square of the altitude.

### (Hypotenuse)

^{2}= (Base)^{2}+ (Altitude)^{2}**Perimeter of Right angled triangle.**### S=a+b+c

**Area of Right angled triangle.**### Area=1/2x base X height

**Properties of Right angled triangle**### 1. The largest angle of a right angle triangle is always 90º

### 2. The largest side of a right triangle is called the hypotenuse which is always the side opposite to the right angle.

### 3. The measurements of the sides follow the Pythagoras rule.

**Types of Right angled triangle**### 1. Isosceles Right Triangle

### 2. Scalene Right Triangle

## Rules for Triangle

**basic rules of a triangle:**

### A triangle has

**three sides**and**three angles.**

The sum of the three interior angles of a triangle is always equal to**Triangle Sum Property:****180 degrees.**

The sum of the length of**Triangle Inequality Theorem:****any two sides**of a triangle is**always greater**than the length of the**third side**.**Exterior Angle Property:****An exterior angle**of a triangle is equal to the**sum of its two interior opposite angles.****Congruent Triangles:****Two triangles**are said to be**congruent**if the lengths of the**corresponding sides**of the triangle are equal.**Similar Triangles:****Two triangles**are said to be**similar**if the lengths of the**corresponding sides**of the triangle are equal.

In a right-angled triangle (a triangle with one 90-degree angle),the**Pythagorean Theorem****square of the length of the hypotenuse**(the side opposite the right angle)**is equal to the sum of the squares of the lengths of the other two sides.**### This theorem is expressed as a^2 + b^2 = c^2, where c represents the length of the hypotenuse, and a and b represent the lengths of the other two sides.

### The side opposite the

**smallest interior angle**is the**shortest side**, and vice versa.### The side opposite the

**largest interior angle**is the**longest side.**

Triangles have several important points called centers. These include the**Triangle Centers****centroid (the point of intersection of the medians),**the**circumcenter (the center of the circle passing through the three vertices),**the**incenter (the center of the circle inscribed inside the triangle),**and the**orthocenter (the point of intersection of the altitudes).**

### Frequently Asked Questions on Triangle Calculator

Let ABC be a triangle such that the length of the 3 sides of the triangle is AB = c, BC = a and CA = b.

the area of triangle ABC = √[s × (s – a) × (s – b) × (s – c)].

Let ABC be a triangle such that the length of the 3 sides of the triangle is AB = c, BC = a and CA = b.

the area of triangle ABC = √[s × (s – a) × (s – b) × (s – c)].

When three sides are given,the following formula can be used to calculate:

cos(α)= b^{2}+c^{2}-a^{2}/2bc

cos(β)= a^{2}+c^{2}-b^{2}/2ac

cos(γ)= a^{2}+b^{2}-c^{2}/2ab

When three sides are given,the following formula can be used to calculate:

cos(α)= b^{2}+c^{2}-a^{2}/2bc

cos(β)= a^{2}+c^{2}-b^{2}/2ac

cos(γ)= a^{2}+b^{2}-c^{2}/2ab

A hypotenuse is the longest side of a right triangle. It's the side that is opposite to the right angle (90°).

Use the Pythagorean theorem to calculate the hypotenuse from the right triangle sides. Take a square root of sum of squares:c = √(a² + b²)

c = √(a² + b²)

A hypotenuse is the longest side of a right triangle. It's the side that is opposite to the right angle (90°).

Use the Pythagorean theorem to calculate the hypotenuse from the right triangle sides. Take a square root of sum of squares:c = √(a² + b²)

c = √(a² + b²)

To find the missing side of a right triangle we use the famous Pythagorean Theorem.

a^{2}+b^{2}=c^{2}

To find the missing side of a right triangle we use the famous Pythagorean Theorem.

a^{2}+b^{2}=c^{2}

The formula for the Perimeter of a Triangle when all sides are given is P= a+b+c.

Where, a, b, c indicates the sides of the triangle.

The formula for the Perimeter of a Triangle when all sides are given is P= a+b+c.

Where, a, b, c indicates the sides of the triangle.

First, find the semi-perimeter of the triangle, s = (a+b+c)/2, where a, b and c are the length of the three sides of the triangle.

Area of the triangle = √[s(s – a)(s – b)(s – c)]

First, find the semi-perimeter of the triangle, s = (a+b+c)/2, where a, b and c are the length of the three sides of the triangle.

Area of the triangle = √[s(s – a)(s – b)(s – c)]

A 30 60 90 triangle is a special right triangle that has interior angles measuring 30°, 60°, and 90°.

A 30 60 90 triangle is a special right triangle that has interior angles measuring 30°, 60°, and 90°.

Subtract the two known angles from 180°,we will get the third angle.

Subtract the two known angles from 180°,we will get the third angle.

The perimeter of any triangle is equal to the sum of all its sides.

It is the total length of any triangle.

Perimeter of ABC = AB + BC + AC

The perimeter of any triangle is equal to the sum of all its sides.

It is the total length of any triangle.

Perimeter of ABC = AB + BC + AC

A 45 45 90 triangle is a special right triangle that has two 45° interior angles and one 90° right angle.

Also called an isosceles triangle.

A 45 45 90 triangle is a special right triangle that has two 45° interior angles and one 90° right angle.

Also called an isosceles triangle.

Pascal's triangle is a number pattern that fits in a triangle.

Named after a French mathematician,Blaise Pascal.

Pascal's triangle is a number pattern that fits in a triangle.

Named after a French mathematician,Blaise Pascal.

Using Pythagorean Theorem we can find out the length of right triangle

c^{2}=a^{2}+b^{2}

Using Pythagorean Theorem we can find out the length of right triangle

c^{2}=a^{2}+b^{2}