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)

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

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P - - R