Mathematics

Problem

\triangle LMN

, right-angled at

M

, the side

LM

measures

7\,\text{cm}

and

\tan L = \dfrac{2}{3}.

Answer the following. a. (i) Determine the lengths of sides

MN

and

LN

. b. (ii) Calculate

\sin L

and

\cos L

. c. (iii) Show that

\sin^{2} L + \cos^{2} L = 1

using the values obtained in part (ii).