In the diagram |LN| = 4cm, LNM = 90o and tan y = ...
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
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