Question

In a triangle LMN, ANGLE M=90°, angle n=30°, LN=12 find the lengths of sides LM and MN

Answer 1

Answer:

In right angled ∆LMN, if ∠N = θ, ∠M = 90°, cos θ = 24/25, find sin θ and tan θ. Similarly, find (sin2 θ) and (cos2 θ). Read more on Sarthaks.com - https://www.sarthaks.com/852893/in-right-angled-lmn-if-n-m-90-cos-24-25-find-sin-and-tan-similarly-find-sin-2-and-cos-2

i. cos θ = 24/25 In ∆LMN, ∠M = 90°, ∠N = θ Let the common multiple be k. ∴ MN = 24k and LN = 25k Now, LN2 = LM2 + MN2 … [Pythagoras theorem] ∴ (25k)2 = LM2 + (24k)2 ∴ 625 k2 = LM2 + 576k2 ∴ LM2 = 625k2 – 576k2 ∴ LM2 = 49k2 ∴ LM = √49k2 ...[Taking square root of both sides] = 7k Read more on Sarthaks.com - https://www.sarthaks.com/852893/in-right-angled-lmn-if-n-m-90-cos-24-25-find-sin-and-tan-similarly-find-sin-2-and-cos-2