In ABC, A is a right angle. And B = 45 degrees. What is the length of BC
A) 54ft
B) 17√ 3ft
C) 17√ 2ft
D) 17ft

The answer would be C

Given that this is an isosceles triangle (triangle with two congruent sides) and is 45 degrees on both sides then this would be considered a 45-45-90 triangle

The rule for this type of triangle is that going from a congruent side (for example segment AC) to BC would result in your multiply by the square root of 2.

Multiplying square roots and whole numbers are fairly easy, just combine it like multiply with a variable. Since the rule for a 45-45-90 triangle is to multiply the side length by the square root of 2 to get the hypotenuse then you would multiply 17 by the square root of 2 which will give you answer choice C.

If you encounter a similar problem like this but with the hypotenuse to the side length then you would do the OPPOSITE of multiplying by the square root of 2 (which would be dividing the hypotenuse by the square root of 2).