I would like to know the biggest rim that will fit my 87 cab

Your Dodge Ram 1500 had options for 3 different rim sizes. They were 17", 20", and 22" rims from the factory. the largest wheel recommendations for handling and speedometer accuracy are as follows;
17" rims = 285 - 70R17
20" rims= 275 - 60R20
22" rims= 285 - 45R22
As a tire size rule, the first number is the millimeter distance from the road to the bottom edge of the rim such as the 285 then the second number say the 45 is the percentage the difference the width is to the height of 285mm. The letter R stands for radial and the last number denotes the size of the rim it fits on.
https://www.sizemytires.com/vehicle/2016/ram/1500

NO a 16" rim fits a 16" tire, and a 17" rim fits a 17" tire
How to Read Tire Sizes Goodyear Auto Service Center
http://www.tirerack.com/tires/tiretech/techpage.jsp?techid=46

if these rims are 13" 5.5jj rims then the biggest tire that you can fit safely is about 195 85 r13
if you go too wide on the tire then the tire beads will not sit properly on the rim and will roll on turns causing a blow out at the worst possible time
talk with a tire shop and get the details on the biggest tire that you can fit legally and safely on the car
after all when it comes to safety , looks can be deadly

Stock Tire - 245/65R17
Revs per Mile:704.3
Overall Diameter: 29.53 in 750.06 mm
Actual Speed: 60 mph 100 km/h

Tire 1 - 275/60R17
Revs per Mile:693.5
Overall Diameter: 29.99 in 761.74 mm
Speedometer1: 59.0 mph 98.4 km/h
Speedometer Difference: 1.557% too slow
Diameter Difference: 1.54%

Will fit with the stock rims.

The tire will fit the rim but your speedometer will not be as accurate as it was due to the lower aspect ratio.

Dont go any bigger than 18s. With rims that big, it will ride like ****, and wear out your wheel bearings, tie rod ends, and more suspension stuff.

as long as you keep the same diamater of the wheel you should be able to put 17 if they make a bolt pattern that fits contact your tire store and they will tell you for sure

most ford pickup rims are 15*7 its kind of a narrow tire therefore the biggest tires are 285/75. those will fit fine too big will rub, crack the sidewall, even cause a blow-out. you can go to your local goodyear and they will lookup your vehicle find the biggest-best tire fore your application, then give you a quote to take with you.

32 10/50 15 on ten inch rims