Answer:
[tex]b=5\sqrt{3}\ units,c=10\ units[/tex]
Step-by-step explanation:
step 1
Find the value of c
we know that
In the right triangle of the figure
The sine of angle of 30 degrees is equal to divide the opposite side to the angle of 30 degrees by the hypotenuse
so
[tex]sin(30^o)=\frac{5}{c}[/tex]
solve for c
[tex]c=\frac{5}{sin(30^o)}[/tex]
Remember that
[tex]sin(30^o)=\frac{1}{2}[/tex]
substitute
[tex]c=\frac{5}{0.5)}[/tex]
[tex]c=10\ units[/tex]
step 2
Find the value of b
Applying the Pythagorean Theorem
[tex]c^2=b^2+5^2[/tex]
substitute the given values
[tex]10^2=b^2+5^2[/tex]
[tex]b^2=10^2-5^2[/tex]
[tex]b^2=100-25[/tex]
[tex]b^2=75[/tex]
[tex]b=\sqrt{75}\ units[/tex]
simplify
[tex]b=5\sqrt{3}\ units[/tex]
therefore
[tex]b=5\sqrt{3}\ units,c=10\ units[/tex]
