The tangent has many practical uses in Physics, Calculus and Engineering, not to mention its importance in understanding fundamental concepts of geometry. The tangent is defined as rise/run or y/x. In right triangles, it is often denoted by the measure of opposite/adjacent. Here's how to convert tangents to degrees.

### Step 1

Figure out the tangent if you don't already know it. With a right triangle, the tangent of an unknown angle in radians is going to be opposite/adjacent. For example, if you have a triangle with hypotenuse=2, opposite=1, adjacent=1.732, your equation would be 1/1.732=.577. So your tangent would be .577 radians.

### Step 2

Use the formula: Tan [Math symbol theta]=opposite/adjacent (rad). Using our example, Tan [Math symbol theta]=.577 rad. In order to determine how many degrees this would be, we need to isolate the angle measurement, [theta].

### Step 3

Divide each side by Tangent, which will isolate your angle measurement. You should then have this equation: [Math symbol theta]=[(opp/adj) rad]/ tan. This is equivilent to saying (opp/adj)*(1/tan). But because 1/tan is simply the reciprocal of tan, we can multiply (opp/adj) and tan^-1, also known as the arctangent. On a calculator, look for the atan or tan^-1 button. Using .577 as the tan in radians, we would have .577*tan^-1=29.985 degrees.

### Step 4

Round to the appropriate decimal place. This usually involves rounding to the nearest degree or tenth of a degree. For example, if you have 29.985 degrees, you would round up to 30 degrees.

### Step 5

Double check your answer. You can check the answer by taking the tangent of your final result in degrees. This is written as follows: tan [final measure in degrees] =?. Using 30 degrees as an example, you have tan 30=?, which results in .577, which is your original number in radians.