Solving Right Angle Triangles

Recall in trigonometric ratios, the Hypotenuse is unique, facing the right angle (90º), however, the Opposite and Adjacent sides depend on the angle (θ)  under consideration. 

For example, side AB is Adjacent in Fig. 4.1.1 while it is the Opposite side in Fig. 4.1.2.

In ΔABC, B and C are complementary angles (i.e. B + C = 90º)

As seen above, if B = θ , then C = 90 – θ

Therefore,

B + C = 90º

B = 90º – C

Sin  θ = Cos (90 – θ ) = \(\frac{b}{a} \)

And Cos θ = Sin (90 – θ ) = \(\frac{c}{a} \)

Example 4.1.1:

Given the diagram below, write down the value of \( \scriptsize tan \: 2\propto \)
Hence calculate the value