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In triangle ABC, A is a right angle, and mB = 45°. Find BC. If your answer is not an integer, leave it in simplest radical form.

The diagram is not drawn to scale.

In triangle ABC A is a right angle and mB 45 Find BC If your answer is not an integer leave it in simplest radical form The diagram is not drawn to scale class=

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AL2006
-- In a right triangle, if ∠B is 45°, then ∠C is too.

-- Since ∠B  and  ∠C  are equal, the sides opposite them
are equal too.  This is an isosceles right triangle.  Its legs
are equal.

-- (The hypotenuse)²  =  (one leg)²  +  (the other leg)²

                                   =       (12-ft)²  +  (12-ft)²

                                   =              (144 x 2)

      The hypotenuse  =  √(144 x 2)  =  12√2 .
meerkat18
Since A is a right angle and mB = 45°, the right triangle is a 45-45-90 triangle.

This means the following:
long leg and short leg have the same value of x
hypotenuse is equal to x√2

Since the long leg has been given as 12 ft. The measure of the short leg is also 12 ft. 

hypotenuse = x√2 = 12 √2 = 12 * 1.414 = 16.97 ft  ⇒ this is the measure of BC.

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