Question

In fgh, fh=9, fg=11 and angle f=65. what is the measure of angle g?

Answer 1

About 48.6 degrees is the answer

Answer 2

The measure of ∠G=48.6°

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=√(81+121-198cos(65))=√(202-198(0.423))=√(202-83.754)=10.87`

By sine rule,

`(sin \angle G)/(9)=(sin\angle 65)/(GH)`

`sin\angle G=9* (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°