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enyata [817]
3 years ago
7

Need help understanding this problem! If someone would explain how to do it that would be great!

Mathematics
1 answer:
Elodia [21]3 years ago
7 0

Answer:

m∠G = 31.83°

Step-by-step explanation:

From the triangle FGH,

FH = 6 ft

FG = 11 ft

And measure of the included angle ∠F = 73°

We have to find the measure of ∠G.

By applying law of cosine in the triangle to get the measure of third side GH first,

GH² = FH² + FG² - 2(FH)(FG)cos(∠F)

GH² = 6² + 11² - 2(6)(11)cos(73°)

GH² = 36 + 121 - 38.593

GH = √118.407

GH = 10.88 ft

Now apply sine rule in the given triangle to get the measure of ∠G.

\frac{\text{sinG}}{FH}=\frac{\text{sinF}}{GH}

\frac{\text{sinG}}{6}= \frac{\text{sin(73)}}{10.88}

sin(G) = 0.527374

G = \text{sin}^{-1}(0.527374)

m∠G = 31.83°

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