Answer:
c = 7[tex]\sqrt{3}[/tex]
Step-by-step explanation:
Using the sine ratio in the left right triangle and the exact value
sin45° = [tex]\frac{\sqrt{2} }{2}[/tex], then
sin45° = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{a}{7\sqrt{2} }[/tex] = [tex]\frac{\sqrt{2} }{2}[/tex] ( cross- multiply )
2a = 14 ( divide both sides by 2 )
a = 7
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Using the tangent ratio in the right triangle and the exact value
tan30° = [tex]\frac{1}{\sqrt{3} }[/tex] , then
tan30° = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{a}{c}[/tex] = [tex]\frac{7}{c}[/tex] = [tex]\frac{1}{\sqrt{3} }[/tex] ( cross- multiply )
c = 7[tex]\sqrt{3}[/tex]
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