Answer:
m = 6[tex]\sqrt{3}[/tex] , n = 6
Step-by-step explanation:
Using the sine and cosine ratios in the right triangle and exact values
cos30° = [tex]\frac{\sqrt{3} }{2}[/tex] , sin30° = [tex]\frac{1}{2}[/tex] , then
cos30° = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{m}{12}[/tex] = [tex]\frac{\sqrt{3} }{2}[/tex] ( cross- multiply )
2m = 12[tex]\sqrt{3}[/tex] ( divide both sides by 2 )
m = 6[tex]\sqrt{3}[/tex]
and
sin30° = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{n}{12}[/tex] = [tex]\frac{1}{2}[/tex] ( cross- multiply )
2n = 12 ( divide both sides by 2 )
n = 6
