Question

In triangle LMN, angle M = 90'
angle L = 30' LN=6 then find MN and LM​

Answer 1

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Answer:

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Answer 2

MN = 3$\sqrt{3}$ cm

LM  = 3cm

Given:

In triangle LMN,

M = 90°

L = 30°

LN= 6

To find:

MN and LM

The sum of angles ∠L + ∠M + ∠N = 180°

∠L + ∠M + ∠N = 180°

30° + 90°+ ∠N = 180°

        120°+ ∠N = 180°

                  ∠N = 180° - 120°

                  ∠N = 60°

Side opposite to 30°

LM = $\frac{1}{2}$ * LN

     = $\frac{1}{2}$ * 6

LM = 3cm

Side opposite to 60°

MN = $\frac{\sqrt{3}}{2}$ * 6

MN = 3$\sqrt{3}$ cm

Therefore, MN = 3$\sqrt{3}$ cm

                  LM = 3cm