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Math Calculators ▶ Law of Sines Calculator
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An online law of sines calculator allows you to find the unknown angles and lengths of sides of a triangle. When we dealing with simple and complex trigonometry sin(x) functions, this calculator uses the law of sines formula that helps to find missing sides and angles of a triangle.
So, read on to get a complete guide about sine laws.
The Laws of sines are the relationship between the angles and sides of a triangle which is defined as the ratio of the length of the side of a triangle to the sine of the opposite angle.
Where:
Sides of Triangle:
$$a = side a, b = side b, c = side c$$
Angles of Triangle:
$$A = angle A, B = angle B, C = angle C$$
Characteristics of Triangle:
P = Triangle perimeter, s = semi-perimeter, K = area, r = radius of inscribed circle, R = radius of circumscribed circle
If a, b, and c are the length of sides of a triangle and opposite angles are A, B, and C respectively; then law of sins shows:
$$a/sinA = b/sinB = c/sinC$$
So, the law of sine calculator can be used to find various angles and sides of a triangle.
Example:
Compute the length of sides b and c of the triangle shown below.
Solution:
Here, calculate the length of the sides, therefore, use the law of sines in the form of
\(\frac{a}{sin A} = \frac{b}{sin B}\)
Now,
$$\frac{a}{sin 100^0}= \frac{12}{sin 50^0}$$
By Cross multiply:
$$12 sin 100^0= a sin 50^0$$
Both sides divide by sin \(50^0\)
$$a = \frac{(12 sin 100^0)}{sin 50^0}$$
From the calculator we get:
$$a = 15.427$$
So, the length of sides b and c is \(15.427 mm\).
However, an Online Sine Calculator will calculate the sine trigonometric function for the given angle in degree, radian, or the π radians.
These are some equations that are used by the law of sines calculator which are obtained from the law of sins:
$$A=sin^{−1}[\frac{asinB}{b}]$$
$$A=sin^{−1}[\frac{asinC}{c}]$$
$$B=sin^{−1}[\frac{bsinA}{a}]$$
$$B=sin^{−1}[\frac{bsinC}{c}]$$
$$C=sin^{−1}[\frac{csinA}{a}]$$
$$C=sin^{−1}[\frac{csinB}{b}]$$
In order to find any side of a triangle law of sines calculator fetched some values from law of sines formula:
$$a=\frac{bsinA}{sinB}$$
$$a=\frac{csinA}{sinC}$$
$$b=\frac{asinB}{sinA}$$
$$b=\frac{csinB}{sinC}$$
$$c=\frac{asinC}{sinA}$$
$$c=\frac{bsinC}{sinB}$$
Also, you can find alpha (α) by using, \(a=n/a, b=n/a, beta (β ) =n/a\) values, while the value of beta is calculated by using \(a=n/a, alpha=n/a, b=n/a\).
An ambiguous case occurs, when two different triangles constructed from given data then the triangles are \(ABC \text{ and} AB’C’\).
There are some conditions to use the law of sines for the case to be ambiguous:
Furthermore, The online CSC Calculator will determine the cosecant and sin inverse trigonometric function for the given angle it either in degree, radian, or the pi (Ï€) radians.
The law of sine calculator especially used to solve sine law related missing triangle values by following steps:
The law of sines calculator calculates:
When you have two sides and one angle or two angles and one side of a triangle then we use laws of sines.
According to the triangle inequality theorem, the sum of any two sides must be greater than the third side of a triangle and this rule must fulfil all three conditions of sides.
An oblique triangle is not a right triangle so basic trigonometric ratios do not apply, they can be modified to cover oblique by using sines and cosines law.
There are different ways to find triangle characteristics:
The law of sines calculator is highly recommendable for assessing the missing values of a triangle by using the law of sines formula. Finding all these values manually is a difficult task, also it increases the risk to get accurate results. By using the law of sine calculator you can find all sine law values instantly and 100% error-free. Moreover, this tool is beneficial for people who work with the law of sine related trigonometric function.
From the source of Wikipedia: The ambiguous case of triangle solution, Relation to the circumcircle, Relationship to the area of the triangle.
From the source of Dave’s Short Trig Course: Oblique Triangles, Pythagorean theorem, Triangle Characteristics.
From the source of Khan Academy: Laws of sines and cosines review, Solving triangles using the law of sines, Missing Angle.
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