The missing sides of the triangle are
GI = 60 units
MH = 34.01 units
IK = 23.07 units
HI = 46.1 units
MG = 34.01 units
How to find the missing sides
The missing sides area solved using properties peculiar to incenter
GI = LI * 2 = 30 * 2 = 60 units (LI = GL)
GI = 60 units
To find MH we use Pythagoras
MH = √(MJ² + JH²) JH = GJ (incentre)
MH = √(14² + 31²)
MH = √(1157)
MH = 34.01 units
Solving for IK
MH = MI = MG (incenter)
using Pythagoras
IK = √(MI² - MK²)
IK = √(1157 - 25²)
IK = √532
IK = 23.07 units
Solving for HI
HI = 2 * IK
HI = 2 * 23.07
HI = 46.14 units
Solving for NG
MH = MI = MG = 34.01 units (incenter)