Answer:
The length of the side opposite the 60 degree angle 'c' = 4
Step-by-step explanation:
Step(i):-
Given data ∠A = 90° , ∠B = 60° and ∠C = 30°
Given data the length of the side opposite the 30 degree angle is 8
let 'a' = 8
step(ii):-
By using sine rule formula in properties of triangle
[tex]\frac{a}{Sin A} = \frac{b}{Sin B} = \frac{c}{Sin C} = 2 R[/tex]
[tex]\frac{a}{Sin A} = \frac{c}{Sin C}[/tex]
[tex]\frac{8}{Sin 90} = \frac{c}{Sin 30}[/tex]
cross multiplication , we get
[tex]\frac{8 X sin 30}{Sin 90} = c[/tex]
we know that trigonometry formulas
sin 30° = [tex]\frac{1}{2}[/tex] and sin 90°= 1
C = 8 X 1/2 = 4
conclusion:-
The length of the side opposite the 60 degree angle 'c' = 4
