Maths MC

Question

Please complete the following MC with explanations.

Answer 1

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The answer is C

BD = √(a2 + a2)

BD = (√2)a

BF = BD = (√2)a

∠BCE = 45˚

By the sin law,

BC / sin∠BFC = BF / sin45˚

a / sin∠BFC = (√2)a / (1/√2)

1/2 = sin∠BFC

∠BFC = 30˚

∠BDE = ∠BFC = 30˚

length of the perpendicular from B to DE

= (√2)a×sin30˚

= (√2)a / 2

= a / √2