Answer :

Answer:

AB = 7

Step-by-step explanation:

Using the cosine ratio in the right triangle and the exact value

• cos45° = [tex]\frac{1}{\sqrt{2} }[/tex] , then

cos45° = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{AB}{AC}[/tex] = [tex]\frac{AB}{7\sqrt{2} }[/tex] = [tex]\frac{1}{\sqrt{2} }[/tex] ( cross multiply )

AB × [tex]\sqrt{2}[/tex] = 7[tex]\sqrt{2}[/tex] ( divide both sides by [tex]\sqrt{2}[/tex] )

AB = 7