Answer:
C
Step-by-step explanation:
Use the sine ratio in the left, right triangle to find the common side to both triangles and the exact values
sin60° = [tex]\frac{\sqrt{3} }{2}[/tex] , cos45° = [tex]\frac{1}{\sqrt{2} }[/tex] , thus
sin60° = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{opp}{7\sqrt{3} }[/tex] = [tex]\frac{\sqrt{3} }{2}[/tex] ( cross- multiply )
2 × opp = 21 ( divide both sides by 2 )
opp = [tex]\frac{21}{2}[/tex]
Now consider the right triangle on the right, using the cosine ratio
cos45° = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{\frac{21}{2} }{x}[/tex] = [tex]\frac{1}{\sqrt{2} }[/tex] ( cross- multiply )
x = [tex]\frac{21}{2}[/tex] × [tex]\sqrt{2}[/tex] = [tex]\frac{21\sqrt{2} }{2}[/tex] → C