Question

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.

Answer 1

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.

Answer 2

-- 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 .