Question

What is the value of each of the angles of a triangle whose sides are a = 87, b = 131, and c = 194 cm in length? (Hint: Consider using the law of cosines.)

α = °

β = °

γ = °

Answer 1

According to Law of Cosines

$c^{2}=a^{2}+b^{2}-2abcos\gamma$

$194^{2}=87^{2}+131^{2}-2*87*131cos\gamma$

$194^{2}-87^{2}-131^{2}=-2*87*131cos\gamma$

$12906=-2*87*131cos\gamma$

$cos\gamma =-12906/22794$

$\gamma =cos^{-1}(-12906/22794)$

ANSWER: ${\color{Red} \gamma =124.49^{\circ}}$

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$a^{2}=b^{2}+c^{2}-2bc*cos\alpha$

$87^{2}=131^{2}+194^{2}-2*131*194*cos\alpha$

$87^{2}-131^{2}-194^{2}=-2*131*194*cos\alpha$

$-47228=-50828*cos\alpha$

$cos\alpha =47228/50828$

$\alpha =cos^{-1}(47228/50828)$

ANSWER: ${\color{Red} \alpha =21.694^{\circ}}$

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Sum of angles inside a triangle is 180 degrees

$\alpha +\beta +\gamma =180^{\circ}$

$21.694^{\circ} +\beta +124.49^{\circ} =180^{\circ}$

$\beta =180^{\circ}-124.49^{\circ}-21.694^{\circ}$

ANSWER: ${\color{Red} \beta =33.816^{\circ}}$

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