Answer:
[tex]7\sqrt{2}[/tex]
Step-by-step explanation:
Here we have to use trigonometry. The best one to use in this case is sine, which is (opposite/hypotenuse), where the opposite is the length of the side opposite to the angle and the hypotenuse is the longest side of the right triangle.
In this case, our angle is the one labeled as 45 degrees. Our opposite side is then 7 and our hypotenuse is b. So, we can write: [tex]sin(45) = 7/b[/tex].
Sin(45) should be a value to memorize; it is equal to [tex]\frac{\sqrt{2} }{2}[/tex] . Substituting this into the equation: [tex]\frac{\sqrt{2} }{2} =\frac{7}{b}[/tex]. Cross multiplying, we get: [tex]\sqrt{2} *b=14[/tex] . So, b = [tex]\frac{14}{\sqrt{2} }[/tex] . To simplify this radical, we multiply the top and bottom by sqrt(2):
[tex]\frac{14*\sqrt{2} }{\sqrt{2}*\sqrt{2}}=\frac{14\sqrt{2} }{2} =7\sqrt{2}[/tex].
Thus, the answer is [tex]7\sqrt{2}[/tex].
Hope this helps!
