in fgh, fh=9, fg=11 and angle f=65. what is the measure of angle g?
Answer:
The measure of ∠G=48.6°
Step-by-step explanation:
In ΔFGH, FH=9 units, FG=11 units and ∠F=65°
Use Cosine Rule to find GH and then Sine Rule to measure of G.
\(GH^2=9^2+11^2-2(9)(11)cos(65)\)
\(GH=81+121-198cos(65)\)
\(GH=\sqrt{81+121-198cos(65)}=\sqrt{202-198(0.423)}=\sqrt{202-83.754}=10.87\)
By sine rule,
\(\frac{sin \angle G}{9}=\frac{sin\angle 65}{GH}\)
\(sin\angle G=9\times \frac{sin\angle 65}{10.87}\)
\(=0.7498704385\)
\(\angle G=sin^{-1}( 0.7498704385)\)
\(=48.57915612\sim 48.6^{\circ}\)
The measure of ∠G=48.6°