Question

solve the right triangle.
write your answers in simplified, rationalized form. do not round.
ab =
bc =
m∠b =°

Explanation:

Step1: Find $\angle B$

Sum of angles in triangle is $180^\circ$.
$m\angle B = 180^\circ - 90^\circ - 45^\circ = 45^\circ$

Step2: Find length of $BC$

Triangle is isosceles ($\angle A=\angle B$), so $BC=AC$.
$BC = 3$

Step3: Find length of $AB$

Use Pythagorean theorem: $AB^2=AC^2+BC^2$.
$$AB = \sqrt{3^2 + 3^2} = \sqrt{18} = 3\sqrt{2}$$

Answer:

$AB = 3\sqrt{2}$
$BC = 3$
$m\angle B = 45^\circ$