Answer:
D). [tex]4\sqrt{2}[/tex]
Step-by-step explanation:
STEP 1a: Find the last angle of the triangle. ( which is angle A)
[tex]A+90+45=180[/tex]
STEP 1b: Solve the equation for A by adding 90 and 45.
[tex]A+135=180[/tex]
STEP 1c: Then Move all terms not containing A to the right side of the equation by subtracting 135 from both sides of the equation
[tex]A=180-135[/tex]
STEP 1d: Subtract 135 from 180.
[tex]A=45[/tex]
STEP 2a: Find side b next.
STEP 2b: The cosine of an angle is equal to the ratio of the adjacent side to the hypotenuse.
[tex]cos(A)=\frac{adj}{hyp}[/tex]
STEP 2c: Substitute the name of each side into the definition of the cosine function.
[tex]cos(A)=\frac{b}{c}[/tex]
STEP 2d: Set up the equation to solve for the adjacent side, in this case b.
[tex]b=c*cos(A)[/tex]
STEP 2e: Substitute the values of each variable into the formula for cosine.
[tex]b=8*cos(45)[/tex]
STEP 2f: Cancel the common factor of 2.
[tex]a=4\sqrt{2}[/tex]
HOPE THIS HELPS!
