Question

ABCD is a square of sides 8cm . M is midpoint of side AB if MCN =45° then find MN .find its solution
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Answer 1

Answer:

MN = 20/3 cm

Step-by-step explanation:

in ΔMBC

∠MCB = θ

Tanθ = MB/BC

MB = 8/2 = 4cm

CD = 8 cm

=> Tanθ = 4/8

=> Tanθ = 1/2

∠MCN = 45°

∠MCN  = ∠MCB  + ∠BCN

=> 45° = θ + ∠BCN

=> ∠BCN = 45° - θ

in Δ BCN

Tan(45 - θ) = BN/BC

=> BN = BC * Tan(45 - θ)

=> BN = 8 * Tan(45 - θ)

Tan(45 - θ) = (1 - Tanθ)/(1 + Tanθ)

using value of Tanθ = 1/2

=>Tan(45 - θ) = (1 - 1/2)/(1 + 1/2)

=>Tan(45 - θ) = 1/3

BN = 8/3

MN = MB + BN

=> MN = 4 + 8/3

=> MN = 20/3 cm