Question

In ∆ABC , <B=90° , <A = 45° and AC = 3√2 cm. The value of BC =? a) √2 cm b) 3cm c) 1cm d) 2cm. ​

Answer 1

Answer: b) 3 cm

Step-by-step explanation:

In $\triangle ABC$, $\angle B=90^\circ, \angle A=45^\circ$, therefore $\angle C=45^\circ$ as the sum of all the angles of a triangle is $180^\circ$.

Since, two angles of the triangle are equal, it is a right angle isosceles triangle right angled at B. Thus, AB = BC = x.

Apply Pythagoras theorem to the triangle.

$\begin{aligned}(AC)^2&=(AB)^2+(BC)^2\\(3\sqrt2)^2&=x^2+x^2\\18&=2x^2\\x^2&=9\\x&=3\end{aligned}$

Thus, the value of BC is 3 cm