Respuesta :
Answer:
a) ∠A = 82.2° , ∠C = 62.8° , c = 17.01
Step-by-step explanation:
Explanation:-
Step(i):-
Given data ∠B measures 35° and the values of a and b are 19 and 11
∠B = 35° and sides a = 19 and b = 11
By using sine rule
[tex]\frac{a}{sin A} = \frac{b}{sin B} = \frac{c}{Sin C} = 2 R[/tex]
now we will use
[tex]\frac{a}{sin A} = \frac{b}{sin B}[/tex]
[tex]\frac{19}{sin A} = \frac{11}{sin 35}[/tex]
cross multiplication , we get
[tex]\frac{19 X sin 35}{11} = sinA[/tex]
sin A = 0.990
A = sin⁻¹( 0.990) = 82.2°
∠A = 82.2°
Step(ii):-
we know that ∠A +∠B +∠C = 180°
∠C = 180° - ∠A -∠B
∠C = 180° -82.2°-35°
∠C = 62.8°
Step(iii):-
we will use formula
[tex]\frac{b}{sin B} = \frac{c}{Sin C}[/tex]
[tex]\frac{11}{sin 35} = \frac{c}{Sin 62.8}[/tex]
[tex]\frac{11 X sin (62.8)}{sin 35} = C[/tex]
c = 17.01
Final answer:-
∠A = 82.2° , ∠C = 62.8° , c = 17.01
