Answer:
c = 45.33, C =97°, a = 40, A = 61.15° , B = 21.85°, b = 17
Step-by-step explanation:
Given that:
C = 97°, a = 40 and b = 17.
We have angle C, we need to find the side the side c opposite to the angle C. we have side a, we need to find the angle A opposite to side a. we have side b, we need to find the angle B opposite to side b.
Using cosine rule:
c² = a² + b² - 2ab × cos(C)
c² = 40² + 17² - 2(40)(17)cos(97)
c² = 2054.74
c = 45.33
Also using sine rule:
[tex]\frac{a}{sin(A)} =\frac{c}{sin(C)} \\\frac{40}{sin(A)}=\frac{45.33}{sin(97)} \\sin(A)=\frac{sin(97))40}{45.33}=0.876\\A=sin^{-1}(0.876)=61.15^0[/tex]
Also:
[tex]\frac{b}{sin(B)} =\frac{c}{sin(C)} \\\frac{17}{sin(B)}=\frac{45.33}{sin(97)} \\sin(B)=\frac{sin(97))17}{45.33}=0.3722\\B=sin^{-1}(0.3722)=21.85^0[/tex]
c = 45.33, C =97°, a = 40, A = 61.15° , B = 21.85°, b = 17
