Finding angle using Tangent


Originally prepared by Steve Seow for

PY 1 Elementary Psychology:

An Introduction to Mind and Behavior

Professor Billy Wooten

Spring 2004

Brown University


Last revised on March 2, 2004


Suppose we know lengths of the two sides of triangle that is connected at a right angle:



To find angle q in degrees, we start with basic trigonometry:



Suppose x is 10 and y is 15, then



If tan q is 0.67, then the inverse of tangent (tan-1) of 0.67 gives us q:



To find tan-1 of 0.67, we need a scientific calculator.


1.      Make sure that the mode of your calculator is set to degrees.

Most calculator has a MODE key. When you press this button, one of the configurable options is to toggle between radian and degrees.


2.      Next, you need to find the inverse tangent key.

Some calculators have an INV key. This is the inverse key. Pressing this key followed by the TAN key gives you the inverse tangent function. Other calculators provide both TAN and TAN-1 on the same key. Typically, you need to press a colored key and then the TAN key to choose the inverse tangent function.


3.      Use your calculator to find TAN-1(1). If your settings are correct, the answer should be 45.


TAN-1(0.67) in our example above should be 33.82. Therefore, q is 33.82o.