Question

In triangle EFG, side G is 9.9 inches, side F is 6.1 inches, and angle F is 32 degrees. Find all possible values of angle G to the nearest tenth of a degree.

A) 32.1°
B) 57.9°
C) 94.3°
D) 127.1°

Answer 1

To find all possible values of angle G in triangle EFG, you can use the Law of Sines. Plugging in the given values, angle G is approximately 57.9°.

Step-by-step explanation:

To find the possible values of angle G, we can use the Law of Sines. The Law of Sines states that in any triangle, the ratios of the lengths of the sides to the sines of their opposite angles are equal. In this case, we have:

Sin(angle F) / side F = Sin(angle G) / side G

Plugging in the given values, we get:

Sin(32°) / 6.1 = Sin(angle G) / 9.9

Now we can solve for angle G:

Sin(angle G) = (Sin(32°) / 6.1) * 9.9

Angle G ≈ arcsin((Sin(32°) / 6.1) * 9.9)

Calculating this value, we find that angle G is approximately 57.9°.