Leases - Schedule of Supplemental Balance Sheet Information Related to Leases (Details) - USD ($) $ in Thousands	Sep. 30, 2020	Mar. 31, 2020
ASSETS
Operating lease ROU assets	$ 53,065	$ 61,461
Operating Lease, Right-of-Use Asset, Statement of Financial Position [Extensible List]	us-gaap:AssetsHeldForSaleNotPartOfDisposalGroupCurrent	us-gaap:OtherAssetsNoncurrent
Finance lease ROU assets, cost	$ 41,682	$ 39,461
Finance Lease, Right-of-Use Asset, Statement of Financial Position [Extensible List]	us-gaap:AssetsHeldForSaleNotPartOfDisposalGroupCurrent	us-gaap:PropertyPlantAndEquipmentNet
Accumulated amortization	$ (21,050)	$ (18,650)
Finance Lease, Liability, Statement of Financial Position [Extensible List]	us-gaap:AssetsHeldForSaleNotPartOfDisposalGroupCurrent	us-gaap:PropertyPlantAndEquipmentMember
Finance lease ROU assets, net	$ 20,632	$ 20,811
Total lease assets	73,697	82,272
Current liabilities:
Operating	$ 15,842	$ 13,139
Operating Lease, Liability, Current, Statement of Financial Position [Extensible List]	tgi:LiabilitiesRelatedToAssetsHeldForSaleCurrent	us-gaap:AccruedLiabilitiesCurrent
Finance	$ 7,215	$ 7,336
Finance Lease, Liability, Current, Statement of Financial Position [Extensible List]	tgi:LiabilitiesRelatedToAssetsHeldForSaleCurrent	us-gaap:LongTermDebtAndCapitalLeaseObligationsCurrent
Noncurrent
Operating	$ 48,121	$ 54,687
Operating Lease, Liability, Noncurrent, Statement of Financial Position [Extensible List]	tgi:LiabilitiesRelatedToAssetsHeldForSaleCurrent	us-gaap:OtherLiabilitiesNoncurrent
Finance	$ 15,122	$ 16,597
Finance Lease, Liability, Noncurrent, Statement of Financial Position [Extensible List]	tgi:LiabilitiesRelatedToAssetsHeldForSaleCurrent	us-gaap:LongTermDebtAndCapitalLeaseObligations
Total lease liabilities	$ 86,300	$ 91,759