What are the exact values of a and b

d) a = 5 ; b = 5√3

Hi there !

30°-60°-90°  Theorem

1)

side opposite the 90° angle = 2a

10 = 2a => a = 10/2 => a = 5  

2)

side opposite the 60° angle => b = 5√3

Good luck !

hope this !

step-by-step explanation:

d = distance between moon and sun, which in this problem is the hypotenuse of a right triangle.  

the distance y is the side opposite to angle x in the right triangle.   use the definition of the sine function from basic trigonometry.

sin(x) = y/d ⇒

d = y/sin(x)