# A triangle has one 90 degrees angle and from there one leg is 10.25 long and the other leg is 7.75 long, what are the degrees for the other two angles?

##### 1 Answer

You can start by using Pythagoras to find the length of the third side to give yourself more options (long way) and then finish off by using SOHCAHTOA* to find the angles:

The triangle you describe is something like this:

It is a **right angled triangle** and we only have **one side** to find (as I will explain the long way), therefore we can easily use Pythagoras to calculate the length of the missing side:

Pythagoras Theorem states:

**Hypotenuse** and

This can be rearranged to find **any** side in **any** right angled triangle, as long as there is only **one** side missing.

Before using Pythagoras, it can be a great help to label the sides

We are missing side

**Remember you are finding #a#, not #a^2# - Square root!**

We can now add this to our triangle:

**Pythagoras - in this question - is unnecessary but can still be done.
**

Now we have all of the sides, we can use

**SOHCAHTOA**:

The Opposite and Adjacent values depend on which angle you are using:

**Opposite** is the side **across** from the angle.

**Adjacent** is the side **on the other side** of the angle.

**Hypotenuse** never changes and is the longest side of the right angled triangle.

Let's label our angles using

Let's look at angle

We could choose any side to use, but let's pretend that we didn't have 12.85 (side

As we look at angle **on the other side** of it is 7.75 (side **across from it** is 10.25 (side **Opposite** and **Adjacent**.

We can use

Therefore:

At this point you use the inverse of Tan (

The other angle can either be found by going through the same process (using **the sum of all angles** in a triangle **must** equal **180°**:

We have **90°** and **52.916°**:

So we can use the following to find the final angle: