Mathematics

Problem

\triangle ABC

, angle

B

is a right angle. The lengths of the two perpendicular sides are

AB = 9\,\text{cm}

and

BC = 12\,\text{cm}.

Answer the following questions related to angle

A

. a. (i) Write the expressions for

\sin A

\cos A

and

\tan A

in terms of the sides of the triangle. b. (ii) Calculate the numerical values of

\sin A

\cos A

and

\tan A

. c. (iii) Using your answers from part (ii), verify that

\tan A = \dfrac{\sin A}{\cos A}

and briefly explain why this relationship holds for any right-angled triangle.