What is the Tallest Mountain in the World?
Further, when measured base-to-peak, Denali / Mount McKinley it is the tallest land-based mountain.
In short, which mountain is the tallest depends on how we measure it.
This BBC Earth documentary explores the question “is Mount Everest really to tallest mountain”, it discusses a number of semantic and geologic concepts that complicate the matter.
Altitude Versus Height Measured Base to Summit
- Mount Everest has an elevation of 8,850 meters (29,035 feet) above sea level. 
- Mauna Kea has an elevation of 4,205 meters (13,796 feet) above sea level. 
The base of Mauna Kea is about 6000 meters below sea level and the summit is about 4000 meters above sea level. The distance between the foot of the mountain and the summit is about 10,000 meters. This makes Mauna Kea the “tallest” mountain in the world. 
The Chimborazo is Farthest from Earth’s Center
- Chimborazo in Ecuador has an elevation of 6,310 meters (20,703 feet) above sea level. However it’s located 6,384 kilometers above Earth’s center making it’s peak about 2 kilometers farther from earths center than Mount Everest. 
Earth isn’t a sphere, it’s an “oblate spheroid” with its widest point at its equator. Chimborazo is just one degree south of the equator. At that location it is 6,384 kilometers above Earth’s center or about 2 kilometers farther from Earth’s center than Mount Everest.
And Then There are the Details
Interestingly enough mountains keep growing, the sea level keeps rising, and other geological happenings keep occurring that make the semantics involved in figuring out the tallest / highest mountain difficult.