Step 1

Given:

Law of sines and law of cosines

Step 2

To determine:

Law of sines and law of cosines with an answer: \(\displaystyle=?\)

Step 3

Solution:

Law of cosines:

It is basically used to calculate the angle(or side length) measurements for triangles other

than right triangles:

Let the sides of the triangle be a, b , c and the included angle is: \(\displaystyle=\alpha\)

Hence,

As per the cosines law:

\(\displaystyle{c}^{{{2}}}={a}^{{{2}}}+{b}^{{{2}}}-{\left({2}{a}{b}\right)}{\cos{\alpha}}\)

So,

Using this law we can easily find the third side;

Step 4

Now:

Law of sines:

It is basically used to find the measure of either angles or the sides of the triangles; This rule is an equation relating the lengths of the sides of the triangle to the sines of its angles; It gives the relationship between the sides and the angles of non-right triangles:

Let a, b and c be the sides of the triangle:

So,

By the law of sines:

\(\displaystyle{\frac{{{\sin{{A}}}}}{{{a}}}}={\frac{{{\sin{{B}}}}}{{{b}}}}={\frac{{{\sin{{C}}}}}{{{c}}}}\)

Where angles A, B and C are the different angles of the triangle.

Given:

Law of sines and law of cosines

Step 2

To determine:

Law of sines and law of cosines with an answer: \(\displaystyle=?\)

Step 3

Solution:

Law of cosines:

It is basically used to calculate the angle(or side length) measurements for triangles other

than right triangles:

Let the sides of the triangle be a, b , c and the included angle is: \(\displaystyle=\alpha\)

Hence,

As per the cosines law:

\(\displaystyle{c}^{{{2}}}={a}^{{{2}}}+{b}^{{{2}}}-{\left({2}{a}{b}\right)}{\cos{\alpha}}\)

So,

Using this law we can easily find the third side;

Step 4

Now:

Law of sines:

It is basically used to find the measure of either angles or the sides of the triangles; This rule is an equation relating the lengths of the sides of the triangle to the sines of its angles; It gives the relationship between the sides and the angles of non-right triangles:

Let a, b and c be the sides of the triangle:

So,

By the law of sines:

\(\displaystyle{\frac{{{\sin{{A}}}}}{{{a}}}}={\frac{{{\sin{{B}}}}}{{{b}}}}={\frac{{{\sin{{C}}}}}{{{c}}}}\)

Where angles A, B and C are the different angles of the triangle.