Respuesta :
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.
[tex]GH^2=9^2+11^2-2(9)(11)cos(65)[/tex]
[tex]GH=81+121-198cos(65)[/tex]
[tex]GH=\sqrt{81+121-198cos(65)}=\sqrt{202-198(0.423)}=\sqrt{202-83.754}=10.87[/tex]
By sine rule,
[tex]\frac{sin \angle G}{9}=\frac{sin\angle 65}{GH}[/tex]
[tex]sin\angle G=9\times \frac{sin\angle 65}{10.87}[/tex]
[tex]=0.7498704385 [/tex]
[tex]\angle G=sin^{-1}( 0.7498704385) [/tex]
[tex]=48.57915612\sim 48.6^{\circ}[/tex]
The measure of ∠G=48.6°
