Answer:
a) ∠A = 82.2° , ∠C = 62.8° , c = 17.01
Step-by-step explanation:
<u><em>Explanation</em></u>:-
<u><em>Step(i)</em></u>:-
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
<em>By using sine rule </em>
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now we will use
![\frac{a}{sin A} = \frac{b}{sin B}](https://tex.z-dn.net/?f=%5Cfrac%7Ba%7D%7Bsin%20A%7D%20%3D%20%5Cfrac%7Bb%7D%7Bsin%20B%7D)
![\frac{19}{sin A} = \frac{11}{sin 35}](https://tex.z-dn.net/?f=%5Cfrac%7B19%7D%7Bsin%20A%7D%20%3D%20%5Cfrac%7B11%7D%7Bsin%2035%7D)
cross multiplication , we get
![\frac{19 X sin 35}{11} = sinA](https://tex.z-dn.net/?f=%5Cfrac%7B19%20X%20sin%2035%7D%7B11%7D%20%3D%20sinA)
<em>sin A = 0.990</em>
<em>A = sin⁻¹( 0.990) = 82.2°</em>
<em> ∠A = 82.2°</em>
<u><em>Step(ii):-</em></u>
we know that ∠A +∠B +∠C = 180°
∠C = 180° - ∠A -∠B
∠C = 180° -82.2°-35°
∠C = 62.8°
<u><em>Step(iii)</em></u>:-
<em>we will use formula</em>
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![\frac{11 X sin (62.8)}{sin 35} = C](https://tex.z-dn.net/?f=%5Cfrac%7B11%20X%20sin%20%2862.8%29%7D%7Bsin%2035%7D%20%3D%20C)
<em>c = 17.01</em>
<u><em>Final answer</em></u>:-
<em> ∠A = 82.2° , ∠C = 62.8° , c = 17.01</em>