Question

What does the law of cosines reduce to when dealing with a right angle

Answer 1

It is reduced to the equation of the Theorem of Pythagoras.

Explanation:

Any triangle can be modelled by this formula under the Law of Cosine:

`b = \sqrt{a^(2)+c^(2)-2\cdot a\cdot c\cdot \cos B}`

Where:

`a`,
`b`,
`c` - Side lengths, dimensionless.

`B` - Angle opposed to the side
`b`, measured in sexagesimal degrees.

Now, let suppose that angle B is a right angle (90º), so that b is a hypotenuse and a and c are legs. Hence:

`\cos B = 0`

And the equation is reduced to the form of the Theorem of Pythagoras, that is to say:

`b = \sqrt{a^(2)+c^(2)}`