# How do you calculate the size of an angle, given the three sides a=5, b=4, c=3?

##### 1 Answer

You know this is a right triangle because

Thus, the side whose length is 5 must be the hypotenuse (it's the largest length.) To find the measure of the angle between the hypotenuse and the side length of 4, you can use the *cosine* function.

cos

so...

cos

thus...

**36.87**

To conclude, the angle between the hypotenuse and the side whose length is 4 is **36.87**. To find the length of the other side, you can subtract the total degree measure of a triangle by 90 (it's a right triangle so at one angle must be 90 degrees.)

total degree measure - the right angle - the angle you just found = the last angle

180 - 90 - 36.87 = **53.13**

**To conclude, the two angles are 36.87 and 53.13.**