Two forces 3

Two forces with magnitudes 8 Newtons and 15 Newtons act at a point. Find the angle between the forces if the resultant force is 17 Newtons.

Correct answer:

A =  90 °

Step-by-step explanation:

$$\begin{gathered} F_1=8\text{N} \\ {F}_2=15\text{N} \\ F=17\text{N} \\ {F}^2=F_1^2+F_2^2-2\cdot F_1\cdot F_2\cdot \cos \alpha \\ \alpha =\arccos (\frac{F_1^2+F_2^2-F^2}{2\cdot F_1\cdot F_2})=\arccos (\frac{8^2+15^2-17^2}{2\cdot 8\cdot 15})\doteq 1.5708\text{rad} \\ A=\alpha \to \text{°}=\alpha \cdot \frac{180}{\pi }\text{°}=1.5708\cdot \frac{180}{\pi }\text{°}=90\text{°}=90^{\circ } \end{gathered}$$

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