Question

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

Answer 1

hello,
given ΔABC with rt∠d at A and ∠B=45°
A+B+C=180°(angle sum property of triangle)
∠C=45°
∴∠B=∠C
∴AB=AC(sides opposite to equal ∠s of triangle are equal)
let AB=AC=x
and ∵ΔABC is rt∠d at A
by Pythagoras Theorem
AB²+AC²=BC²
=x²+x²=BC²
BC²=2x²
BC=√2x²
BC=x√2 unit
hope this helps

Answer 2

In ∆ABC

Angle A = 90°, angle B = 45°

By triangle property,

Angle A + Angle B + Angle C = 180°:

90° + 45° + Angle C = 180°:

Angle C = 45°

Therefore, ∆ ABC is an isosceles ∆

where AB = AC = x (let)

By phythagoras theorem,

(AB)^2 + (AC)^2 = (BC)^2:

(x)^2 + (x)^2 = (BC)^2:

2(x)^2 = (BC)^2:

BC = x × √2