Triangle Calculator Online
Find Missing Angles and Sides of A Triangle. Solve SSS, SAS, SSA using the Triangle Calculator.
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) = (b2 + c2 − a2) / 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) = (c2 + a2 − b2)/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:a2 = b2 + c2 − 2bc cosA
Example:Two sides are 5,7 and Angle 49°
a2 = 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
A triangle has three sides and three angles.
Triangle Sum Property:
The sum of the three interior angles of a triangle is always equal to 180 degrees.Triangle Inequality Theorem:
The sum of the length of 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.Pythagorean Theorem
In a right-angled triangle (a triangle with one 90-degree angle),the 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.
Triangle Centers
Triangles have several important points called centers. These include the centroid (the point of intersection of the medians),the circumcenter (the center of the circle passing through the three vertices),theincenter (the center of the circle inscribed inside the triangle), and theorthocenter (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)= b2+c2-a2/2bc
cos(β)= a2+c2-b2/2ac
cos(γ)= a2+b2-c2/2ab
When three sides are given,the following formula can be used to calculate:
cos(α)= b2+c2-a2/2bc
cos(β)= a2+c2-b2/2ac
cos(γ)= a2+b2-c2/2ab
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.
a2+b2=c2
To find the missing side of a right triangle we use the famous Pythagorean Theorem.
a2+b2=c2
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
c2=a2+b2
Using Pythagorean Theorem we can find out the length of right triangle
c2=a2+b2
