Answer:
a = 15.99793448 or 16
∠B = 23.92706149° or 24°
∠C = 44°
Step-by-step explanation:
Given: Missing:
∠A = 112° ∠B = ?b = 7 ∠C = ?c = 12 a = ?
Solve side A first.
a² = b² + c² - 2bc cos A
a² = 7² + 12² - 2 (7) (12) cos (112°)
√a² = √255.9339077
Now, solve for ∠B.
cos B = [tex]\frac{a^{2} + c^{2} - b^2}{2ac}[/tex]
cos B = [tex]\frac{16^2+12^2-7^2}{2(16)(12)}[/tex]
cos B = 0.9140625
cos[tex]^{-1}[/tex](0.9140625)
Lastly ∠C
To solve ∠C:
∠A+∠B+∠C = 180°
112° + 24° +∠C =180°
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Answers & Comments
Answer:
a = 15.99793448 or 16
∠B = 23.92706149° or 24°
∠C = 44°
Step-by-step explanation:
Given: Missing:
∠A = 112° ∠B = ?
b = 7 ∠C = ?
c = 12 a = ?
Solve side A first.
a² = b² + c² - 2bc cos A
a² = 7² + 12² - 2 (7) (12) cos (112°)
√a² = √255.9339077
a = 15.99793448 or 16
Now, solve for ∠B.
cos B = [tex]\frac{a^{2} + c^{2} - b^2}{2ac}[/tex]
cos B = [tex]\frac{16^2+12^2-7^2}{2(16)(12)}[/tex]
cos B = 0.9140625
cos[tex]^{-1}[/tex](0.9140625)
∠B = 23.92706149° or 24°
Lastly ∠C
To solve ∠C:
∠A+∠B+∠C = 180°
112° + 24° +∠C =180°
∠C = 44°