NECO 2023 · Paper 1 · Q36

Statics: forces, equilibrium & moments

Two forces $X$ and $Y$ have magnitudes 15 N and 20 N respectively, and their resultant is $R$ . If the angle between $X$ and $R$ is $30^\circ$ , what is the angle between $X$ and $Y$ , to the nearest degree?

Worked solution (try it first)

Draw $X$ and $Y$ head to tail.
$R$ closes the triangle.
Its sides are 15, 20 and $R$ .
The $30^\circ$ between $X$ and $R$ is opposite the side $Y = 20$ .
Let $\phi$ be the angle opposite $X = 15$ .
Sine rule: $\sin\phi = \dfrac{15\sin30^\circ}{20}$
$= 0.375$ , so $\phi = 22.0^\circ$ .
The angle between $X$ and $Y$ is the outside angle of the triangle where they meet, which equals the two opposite inside angles added: $30^\circ + 22.0^\circ \approx 52^\circ$ , option C.

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