In the diagram |LN| = 4cm, LNM = 90o and tan y = \(\frac{2}{3}\). What is the area of the \(\bigtriangleup\)LMN?

In the diagram |LN| = 4cm, LNM = 90o and tan y = \(\frac{2}{3}\). What is the area of the \(\bigtriangleup\)LMN?

A.

24cm2

B.

12cm2

C.

10cm2

D.

6cm2

Correct answer is B

Since tan y = \(\frac{2}{3}\) and LN = 4

tan y = \(\frac{2 \times 4}{3 \times 4} = \frac{8}{12} = \frac{4}{6}\)

then tan y = \(\frac{opp}{adj}\)

MN = 6cm

Area of angle LMN = \(\frac{1}{2}\)bh

= \(\frac{1}{2} \times 6 \times 4\)

= 12cm3