Question

Question

On a piece of paper, use a protractor to construct right triangle ABC with AB=3 in., m∠A=90°, and m∠B=45°.

What statement is true about the triangle?

A/1).AC=3 in.
B/2).BC=3 in.
C/3).BC=6 in.
D/4).AC=6 in.

Answer 1

AC=3 in.

Explanation:

It is given in the figure attached, in Δ ABC

∠ A = 90°

m∠B = 45°

AB = 3 in.

We have to find all sides of the triangle given

we will apply sine in Δ ABC to find the measure of AC

sinB =

Now by cross multiplication

BC = 3√2 in.

Now by Pythagoras theorem

BC²= AC² + AB²

(3√2)² = AC² + 3²

18 - 9 = AC²

AC = √9 = 3

Now we come to the options you have mentioned

AC = 3 in. is the correct answer.