Answer:
b = 5.3
A = 48.6
B = 41.4
Step-by-step explanation:
Attached is the Pics contain the Pythagoras Theorem and Trigonometric Identities.
So for our Right-Angled Triangle we have from Pythagoras Identity that
[tex]a^{2} +b^{2} =c^{2}[/tex] ,, Then [tex]b^{2} =c^{2} -a^{2}[/tex] where a=6 , c=8
by substituting,
[tex]b^2=8^2-6^2=28\\ b=\sqrt{28} =2\sqrt{7}=5.3[/tex]
Now to find A , we will use the Trigonometric Identities
Since [tex]sin(A)=\frac{Opposite}{Hypotenuse}=\frac{a}{c} =\frac{6}{8}=\frac{3}{4} \\[/tex]
[tex]A=sin^{-1} (\frac{3}{4} )=48.6\\[/tex]
Since in any Triangle A+B+C=180
Then B=180-A-C=180-48.6-90=41.4
