You're correct, there should be a transaction log backup scheduled to take full advantage of the 'full' recovery model. You don't have to, but it doesn't make sense otherwise. If it's not being done, you might as well use the 'simple' recovery model.
If you have access to the SQL server (and you're allowed to do so), this script will spill the beans on the backup situation for any database.
Put your database name in the @mydatabase variable in the script.
Usual disclaimers, etc.
DECLARE @mydatabase as varchar(100)
set @mydatabase = 'your database name goes here'
SELECT sysdb.name, bkup.description, bkup.backup_finish_date,
when type='D' then '** FULL **'
when type='I' then 'DIFFERENTIAL'
when type='L' then 'LOG'
end as Backup_Type,
(STR(ABS(DATEDIFF(day, GetDate(),(backup_finish_date))))) as 'Days_Ago',
ceiling(bkup.backup_size /1048576) as 'Size MB' ,
cast((bkup.backup_size /1073741824) as decimal (9,2)) as 'Size GB',
,datediff(minute, bkup.backup_start_date, bkup.backup_finish_date) as 'Mins'
,cast(cast(datediff(minute, bkup.backup_start_date, bkup.backup_finish_date)
as decimal (8,3))/60 as decimal (8,1)) as 'Hours', first_lsn, last_lsn, checkpoint_lsn
FROM master.dbo.sysdatabases sysdb LEFT OUTER JOIN msdb.dbo.backupset bkup ON bkup.database_name = sysdb.name
where backup_finish_date > DATEADD(DAY, -60, (getdate())) -- Last 60 days
AND sysdb.name = @mydatabase
ORDER BY sysdb.name, bkup.backup_finish_date desc