Question

In ΔEFG, g = 970 inches, f = 930 inches and ∠F=121°. Find all possible values of ∠G, to the nearest degree.

Answer 1

To solve this question we will use the Sine Law:

`(\sin \measuredangle G)/(g)=(\sin \measuredangle F)/(f)=(\sin \measuredangle E)/(e)\text{.}`

Substituting g=970in, f=930in, and ∡F=121° we get:

`(\sin\measuredangle G)/(970in)=(\sin121^(\circ))/(930in)\text{.}`

Multiplying the above equation by 970in we get:

`\begin{gathered} (\sin\measuredangle G)/(970in)*970in=(\sin121^(\circ))/(930in)*970in, \\ \sin \measuredangle G=(970)/(930)\sin 121^(\circ)\text{.} \end{gathered}`

Therefore:

`\begin{gathered} \measuredangle G=\sin ^(-1)((970)/(930)\sin 121^(\circ)) \\ \measuredangle G\approx63^(\circ). \end{gathered}`

Answer:

`63^(\circ).`