Question

What is the equation if one of the acute angles of a right angled traingle s 38 degrees more than the other?

Answer 1

`alpha + beta = 90`
`alpha - beta = 38`

Explanation:

Let's call the angles `alpha`, `beta` and `gamma`. For every triangle, we have

`alpha + beta + gamma = 180`

But we have a right triangle, so one of the angles - say `gamma` - is right: `gamma = 90`

So, our equation becomes

`alpha + beta + 90 = 180`

`\implies alpha + beta = 180 - 90`

`\implies alpha + beta = 90`

Moreover, we know that one of the angles - say `alpha` - is 38 degrees more than the other:

`alpha = beta + 38`

`implies alpha - beta = 38`

We have the system which describes the situation:

`alpha + beta = 90`
`alpha - beta = 38`