Find the value of c.
a. 10
b. 5
c. √2
d. 10√2
i need this asap ty!

The side C equals to 10. hence the answer is letter A

Step-by-step explanation:

To solve this, we need to use trigonometric functions.

we know that sin (α) = Lo / H for a triangle. Being Lo : Length of the opposite side and H: Length of the hypotenuse.

Given α= 45º and Lo= 5√2 and replacing in the equation:

sin (45º) = 5√2 / C (1)

Using trigonometric identities we know that sin(45º) =(√2)/2. Replacing in equation (1):

sin (45º) = (√2)/2 = 5√2 / C ⇒ C = 2 *5 *√2 / (√2) ⇒ C=10