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In AABC, m/A = 74, a = 59.2, and c = 60.3. What are the two possible values for m/C, to
the nearest tenth?
1) 73.7 and 106.3
2) 73.7 and 163.7
3) 78.3 and 101.7
4)78.3 and 168.3

In AABC mA 74 a 592 and c 603 What are the two possible values for mC to the nearest tenth 1 737 and 1063 2 737 and 1637 3 783 and 1017 4783 and 1683 class=

Respuesta :

Answer:

option 3

Step-by-step explanation:

using the Sine Rule in Δ ABC

[tex]\frac{a}{sinA}[/tex] = [tex]\frac{c}{sinC}[/tex] , that is

[tex]\frac{59.2}{sin74}[/tex] = [tex]\frac{60.3}{sinC}[/tex] ( cross- multiply )

59.2 × sinC = 60.3 × sin74° ( divide both sides by 59.2 )

sinC = [tex]\frac{60.3sin74}{59.2}[/tex] , then

∠ C = [tex]sin^{-1}[/tex] ([tex]\frac{60.3sin74}{59.2}[/tex] ) ≈ 78.3° ( to the nearest tenth )

or ∠ C = 180° - 78.3° = 101.7°