In the diagram |LN| = 4cm, LNM = 90o and tan y = \(\frac{2}{3}\). What is the area of the \(\bigtriangleup\)LMN?
Attached Figure / Diagram
A
24cm2
B
12cm2
C
10cm2
D
6cm2
Verified Correct Answer: B.
Step-by-Step Mathematical Solution
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
Source: Myschool Past Questions Archive (Record #36296)