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Law of sines

# Law of sines

The Law of Sines is the relationship between sides and angles in any triangle.

The sides of a triangle are to one another in the same ratio as the sines of their opposite angles.

Let's see...

Consider this triangle:

Then, the Law of Sines states that:

The law can also be written as the reciprocal:

Proof:

The perpendicular, oc, splits this triangle into two right-angled triangles. This lets us calculate h in two different ways

• Using the triangle cao gives
• Using the triangle cbo gives
• Eliminate h from these two equations
• Rearrange

By using the other two perpendiculars the full law of sines can be proved. QED.

Find c

$\frac{sin50}{10}$ = $\frac{sin88}{c}$ ; c·sin50=10·sin88; c=$\frac{10sin88;}{sin50}$ ; c=13.05

Find the value of the missing angle (Round the solution to hundredths).
 =? =4 =30 =10

The value of the missing side is: