Loonie

Loonie has three wooden sticks measuring 17 inches, 21 inches, and 25 inches. He lays them down to form a triangle. Find the measure of the angle enclosed by 17 inches and 21 inches. (Express answers to the nearest hundredths) (using the law of cosines)

Correct answer:

γ =  81.5435 °

Step-by-step explanation:

$$\begin{gathered} a=17\text{in} \\ b=21\text{in} \\ c=25\text{in} \\ {c}^2=a^2+b^2-2\cdot a\cdot b\cdot \cos \gamma \\ 2\cdot a\cdot b\cdot \cos \gamma =a^2+b^2-c^2 \\ k=\cos \gamma \\ k=\frac{a^2+b^2-c^2}{2\cdot a\cdot b}=\frac{17^2+21^2-25^2}{2\cdot 17\cdot 21}=\frac{5}{34}\doteq 0.1471 \\ \gamma =\frac{180°}{\pi }\cdot \arccos k=\frac{180°}{\pi }\cdot \arccos 0.1471=81.5435^{\circ }=81°32^{\prime }37" \end{gathered}$$

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