Answer:
AC=3 in, m∠C=45° and BC=3√2 in.
Step-by-step explanation:
Given information: ABC is a right angled triangle AB=3 in. , m∠A=90° , and m∠B=45° .
According to the angle sum property the sum of interior angles of a triangle is 180°.
\(\angle A+\angle B+\angle C=180^{\circ}\)
\(90^{\circ}+45^{\circ}+\angle C=180^{\circ}\)
\(135^{\circ}+\angle C=180^{\circ}\)
\(\angle C=180^{\circ}-135^{\circ}\)
\(\angle C=45^{\circ}\)
The measure of angle C is 45°.
In a right angled triangle,
\(\tan\theta=\frac{opposite}{adjacent}\)
In triangle ABC,
\(\tan B=\frac{AC}{AB}\)
\(\tan (45^{\circ})=\frac{AC}{3}\)
\(1=\frac{AC}{3}\)
Multiply both sides by 3.
\(3=AC\)
The measure of AC is 3 in.
According to Pythagoras theorem,
\(hypotenuse^2=base^2+perpendicular^2\)
\(BC^2=3^2+3^2\)
\(BC^2=9+9\)
\(BC^2=18\)
Taking square root on both sides.
\(BC=\sqrt{18}\)
\(BC=3\sqrt{2}\)
Therefore, the missing measurements are AC=3 in, m∠C=45° and BC=3√2 in.
