# Math

Hey guys! Just asking for some quick help.
In ABC , A is a right angle, and B = 45 degrees. What is the length of BC? If the answer is not an integer leave it in simplest radical form. The diagram has 11ft listed as height of the tall side

11ft
11 sqrt 2
11 sqrt 3
22ft

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1. isosceles right triangle, 90 + 45 + 45 = 180
1^2 + 1^2 = 1+1 = 2
so ratios are 1, 1, sqrt 2
we want the hypotenuse
11 * sqrt 2

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2. It looks like BC is the hypotenuse.
method 1:
BC/11 = sin45
BC = 11sin45 = 11/(√2/2)
= 22/√2 * √2/√2
= 22√2 / 2 = 11√2

method 2:
BC^2 = 11^2 + 11^2
= 242
BC = √242 = 11√2

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