Using Pythagorean Theorem, we can write:
[tex]\begin{gathered} \text{Leg}^2+\text{AnotherLeg}^2=\text{Hypotenuse}^2 \\ b^2+6^2=14^2 \\ b^2+36=196 \\ b^2=196-36 \\ b^2=160 \\ b=\sqrt[]{160} \\ b\approx12.6 \end{gathered}[/tex]
Now, let's find the angles.
Sin is the ratio of opposite to hypotenuse
Cos is the ratio of adjacent to hypotenuse
Tan is the ratio of opposite to adjacent
Let's find angle B:
[tex]\begin{gathered} \cos B=\frac{BC}{AB} \\ \cos B=\frac{6}{14} \\ \cos B=0.42857 \\ B=\cos ^{-1}(0.42857) \\ B=64.6\degree \end{gathered}[/tex]
Now, we know three angles in a triangle add to 180 degrees, thus we can say:
[tex]\begin{gathered} A+B+90=180 \\ A+B=180-90 \\ A+B=90 \\ A+64.6=90 \\ A=90-64.6 \\ A=25.4\degree \end{gathered}[/tex]
The answers are:
b = 12.6A = 25.4°B = 64.6°
