Answer:
a = 7, b = [tex]\frac{7\sqrt{3} }{3}[/tex]
Step-by-step explanation:
Using the sine ratio in the left right triangle and the exact value
sin45° = [tex]\frac{1}{\sqrt{2} }[/tex] , then
sin45° = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{a}{7\sqrt{2} }[/tex] = [tex]\frac{1}{\sqrt{2} }[/tex] ( cross- multiply )
a × [tex]\sqrt{2}[/tex] = 7[tex]\sqrt{2}[/tex] ( divide both sides by [tex]\sqrt{2}[/tex] )
a = 7
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Using the tangent ratio in the right triangle on the right and the exact value
tan60° = [tex]\sqrt{3}[/tex] , then
tan60° = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{a}{b}[/tex] = [tex]\frac{7}{b}[/tex] = [tex]\sqrt{3}[/tex] ( multiply both sides by b )
b × [tex]\sqrt{3}[/tex] = 7 ( divide both sides by [tex]\sqrt{3}[/tex] )
b = [tex]\frac{7}{\sqrt{3} }[/tex] × [tex]\frac{\sqrt{3} }{\sqrt{3} }[/tex] = [tex]\frac{7\sqrt{3} }{3}[/tex]
