Answer:
x = 14
Step-by-step explanation:
Using the sine ratio in the right triangle and the exact value of sin45°
sin45° = [tex]\frac{\sqrt{2} }{2}[/tex]
Hence
sin45° = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{7\sqrt{2} }{x}[/tex]
Multiply both sides by x
x × sin45° = 7[tex]\sqrt{2}[/tex] ( divide both sides by sin45° )
x = [tex]\frac{7\sqrt{2} }{sin45}[/tex]
= [tex]\frac{7\sqrt{2} }{\frac{\sqrt{2} }{2} }[/tex]
= 7[tex]\sqrt{2}[/tex] × [tex]\frac{2}{\sqrt{2} }[/tex] = 7 × 2 = 14
