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What is Tan 45 degrees?

Tan is short for tangent. Here we tell you what tan 45 degrees is, how we came up with the answer, and how knowing tan of 45 degrees can be useful.

To calculate tan (45) degrees of a right angled triangle, we use the following equation where angle is 45:

Tan(angle) = Opposite/Adjacent

Tan 45 degrees is simply the ratio of the side opposite of the angle to the side adjacent to the angle. As long as the angle stays at 45 degrees, the ratio does not change and tan 45 degrees is a fixed number. See figure 1 for a better illustration. The answer to "What is tan 45 degrees?" is as follows:

Tan(45) = 1.000

Now you also know that the following is true:

1.000 = Opposite/Adjacent

This is useful because if you know either Opposite or Adjacent length, you can enter it in the equation above and solve for the missing length.

You can also re-write the equation above to solve for Opposite and Adjacent to get the following new equations:

Opposite = 1.000 x Adjacent

Adjacent = Opposite / 1.000

Figure 1

Tan of the angle in the illustration above is calculated by dividing the length of the Opposite by the length of the Adjacent.

If the angle is 45, then the tan of 45 degrees will be 1.000.

More information from Research Maniacs:

Tan Calculator
Go here to find the tan of a different angle.

What is Tan 46 degrees?
Go here for the next angle we converted.


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