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 (Ξ±) = Lo / H for a triangle. Being Lo : Length of the opposite side and H: Length of the hypotenuse.
Given Ξ±= 45ΒΊ and Lo= 5β2 and replacing in the equation:
sin (45ΒΊ) = 5β2 / C (1)
Using trigonometric identities we know that sin(45ΒΊ) =(β2)/2. Replacing in equation (1):
sin (45ΒΊ) = (β2)/2 = 5β2 / C β C = 2 *5 *β2 / (β2) β C=10