# Answer on Trigonometry Question for Ali

Question #1203

Question:

Solve ∆ABC, if a=29.3°, b=20.5cm, and a=12.8cm. round the side length to nearest tenth of centimeter angles degree, if necessary. include all solutions.

Solve ∆ABC, if a=29.3°, b=20.5cm, and a=12.8cm. round the side length to nearest tenth of centimeter angles degree, if necessary. include all solutions.

Expert's answer

According to the law of cosines:

c

c = 11.24

Then let's use the law of sines:

a/c = sin (γ)/sin (α); b/c = sin (β)/sin (α);

Thus

γ = arcsin(a/c * sin (α)) = 33.8°

β = arcsin(b/c * sin (α)) = 63.2°

c

^{2}= a^{2}+ b^{2}- 2ab cos (∠ a) =12.8^{2}+ 20.5^{2}- 2*12.8*20.5 cos(29.3°) = 126.428c = 11.24

Then let's use the law of sines:

a/c = sin (γ)/sin (α); b/c = sin (β)/sin (α);

Thus

γ = arcsin(a/c * sin (α)) = 33.8°

β = arcsin(b/c * sin (α)) = 63.2°

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