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

Mathematics
WAEC 2007

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
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Correct Answer: Option B
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

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