Home » » In the diagram |LN| = 4cm, LNM = 90o and tan y = $$\frac{2}{3}$$. What is the ar...

In the diagram |LN| = 4cm, LNM = 90o and tan y = $$\frac{2}{3}$$. What is the ar...

Question

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

Explanation:

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

Dicussion (1)

• 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