Answer:
Part 1) [tex]BC=18\ in[/tex]
Part 2) [tex]AC=24\ in[/tex]
Part 3) [tex]AB=30\ in[/tex]
Step-by-step explanation:
see the attached figure to better understand the problem
step 1
Find BC
we know that
In the right triangle ABC
[tex]sin(A)=\frac{BC}{AB}[/tex] ----> by SOH (opposite side divided by the hypotenuse)
we have
[tex]AB=30\ in[/tex] ----> the hypotenuse (greater side)
substitute the given values
[tex]\frac{3}{5}=\frac{BC}{30}[/tex]
[tex]BC=\frac{3}{5}(30)=18\ in[/tex]
step 2
Find AC
In the right triangle ABC
Applying the Pythagorean Theorem
[tex]AB^2=BC^2+AC^2[/tex]
substitute the given values
[tex]30^2=18^2+AC^2[/tex]
[tex]AC^2=30^2-18^2[/tex]
[tex]AC^2=576\\AC=24\ in[/tex]
