Question

is it possible to build a triangle using the given side lengths? if so, list the angles of the triangle in order from least to greatest measure. PQ=sqrt (58), QR=2sqrt (13), PR=5sqrt (2)

Answer 1

To build a triangle we need that the sum of any two given sides to be greater than the third side.
PQ+QR=
sqrt(58)+2sqrt(13)=14.82687566 >PR ✅
QR+PR=
2sqrt(13)+5sqrt(2)=14.28217036 >PQ✅
PQ+PR=
Sqrt(58)+5sqrt(2)=14.68684092>QR✅
So YES we can make a triangle with those dimensions

The least angle will be opposing the least side so will have
Angle PQR, angleQPR, angleQRP
Q
/\
/ \
P—— R