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Math Calculators ▶ Law of Sines Calculator
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 (π) 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.
Everybody needs a calculator at some point, get the ease of calculating anything from the source of calculator-online.net. Feel free to contact us at your convenience!
