Question

select the correct answer.
consider triangle efg.
what is the approximate measure of angle g?
a. 55.8°
b. 82.8°
c. 41.4°
d. 94.8°

Explanation:

Step1: Identify sides for angle G

Side opposite angle G: EF = 8; side adjacent: FG = 12

Step2: Apply Law of Sines

$\frac{\sin G}{EF} = \frac{\sin E}{FG}$? No, use Law of Sines correctly: $\frac{\sin G}{EF} = \frac{\sin (\text{angle opposite FG})}{EG}$? Wait, correct: In △EFG, sides: EF=8, FG=12, EG=10. Angle G is opposite EF=8.

Step3: Law of Cosines for angle G

$\cos G = \frac{FG^2 + EG^2 - EF^2}{2 \cdot FG \cdot EG} = \frac{12^2 + 10^2 - 8^2}{2 \cdot 12 \cdot 10} = \frac{144+100-64}{240} = \frac{180}{240}=0.75$

Step4: Calculate angle G

$G = \arccos(0.75) \approx 41.4^\circ$

Answer:

C. 41.4°