Question

Solve the following
In ∆LMN, L-60° M = 30°, LM - 15 cm. Find LN and MN.

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Answer 1

Given :- In ∆LMN, L = 60°, M = 30°, LM = 15 cm .

To Find :- LN and MN.

Solution :-

in ∆LMN we have,

→ ∠L + ∠M + ∠N = 180° (By angles sum property.)

→ 60° + 30° + ∠N = 180°

→ ∠N = 180° - 90°

→ ∠N = 90°

so, ∆LNM is a right angled ∆ .

then, in right angled ∆LNM we have,

→ sin 30° = LN / LM

→ 1/2 = LN / 15

→ 2LN = 15

→ LN = 7.5 cm . (Ans.)

and,

→ cos 30° = MN / LM

→ √3/2 = MN / 15

→ 2MN = 15√3

→ MN = 7.5√3 cm . (Ans.)

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