1. Measurement – Right Angled Triangles By the end of this lesson you will be able to identify and calculate the following: 1. Inverse TAN (TAN -1 )

2.  If the value of the tangent of an angle is known, the size of this angle can be found with the aid of either a scientific or a graphics calculator.  Know that tan θ = 0.5862, then the value of θ can be obtained by ‘undoing’ the tangent function. inverse of tangenttan −1  The inverse of tangent, denoted by tan −1 ‘undoes’ the tan, thus leaving θ on its own.

3.  You will notice that the tangent inverse, tan −1 is written above the tan button in a different colour.  When finding the inverse tangent ratio, the answer is the angle that has that ratio.  In general we give angles correct to the nearest degree (whole number).

4.  The size of any angle in a right-angled triangle can be found using the tangent ratio if the lengths of the two sides adjacent to the right angle are known.  Follow these steps: 1. Label the sides of the triangle with respect to the angle to be found using the symbols O, A and H. 2. Use the tangent ratio to write a relationship between the opposite and the adjacent sides. 3. Find the size of the angle using the inverse tangent function.