Question

N ΔABC, ∡A is a right angle, and m∡B = 45°.

What is the length of BC? If the answer is not an integer, leave it in simplest radical form. The diagram is not drawn to scale.
A. 13 square root 2 ft
B. 13 square root 3 ft
C. 26 ft
D. 13 ft

SOMEONE PLEASE HELP QUICK!

Answer 1

A

Explanation:

remember, the sum of all angles in any triangle is always 180°.

it is a right-angled triangle (angle A = 90°).

angle B = 45°.

that leaves for angle C

angle C = 180 - 90 - 45 = 45°.

so, angle B = angle C.

and that makes AB = AC = 13 ft

Pythagoras then tells us

a² + b² = c²

c being the Hypotenuse (the baseline opposite of the 90° angle). a and b are the legs.

so,

BC² = AC² + AB² = 13² + 13² = 169 + 169 = 2×169 = 338

BC = sqrt(338) = sqrt(2×169) = 13×sqrt(2)