Two teams are pulling a heavy chest, located at point X. The teams are 4.6 meters away from each other. Team A is 2.4 meters away from the chest, and Team B is 3.2 meters away. Their ropes are attached at an angle of 110°. Law of sines:

According to the law of sines, the provided data, and the names assigned to each side and angle, the part of the equation we use is [tex]\\ Sin 110 / 4.6 = Sin C / 3.2[/tex].

What is the Law of sines?

The law of sines is a way to establish a relationship between the angles of a triangle and its corresponding sides.

Each side is related to the sine of the angle. This is,

A triangle has three angles, let us call them A, B, and C

Each angle has its side placed opposite to them. We will call them sides a, b, and c.

The Law of sines states that

[tex]\\ \\ a/sin A = b/sin B = c/ sin C[/tex]

or, you can also write it the other way,

[tex]\\ sinA / a = sinB / b = sinC / c[/tex]

When can be use the Law of senes?

We can use the law of senes in any type of triangle.

Usually, we use it in triangles that are not rectangles (this is because usually, we use the Pythagoras theorem when we have a rectangle triangle)

We can use the law of sines when we know

a pair of data ⇒ one of the angles and the length of its side

any other data ⇒ an angle or one of the sides

For the exposed example, you will find the complete explanation in the attached files.

You will see the assigned names for each side and angle, which can differ from yours. Please, pay attention to this when answering your question.

According to the provided information, the law of sines and the assigned names for each side and angle, the part of the equation we use is [tex]\\ Sin 110 / 4.6 = Sin C / 3.2[/tex]

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