If ∠G measures 45°, ∠F measures 82°, and f is 7 feet, then find g using the Law of Sines. Round your answer to the nearest foot. triangle EFG with side e across from angle E, side f across from angle F, and side g across from angle g 4 feet 5 feet 6 feet 7 feet

The value of g across from angle G is 5feet

According to sine rule

Given the following

∠G = 45°

∠F = 82°

f = 7feet

Required

side g

Substitute the given values into the formula

Hence the value of g across from angle G is 5feet

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The length of the line segment EF () is approximately 5 feet.

Let be a Triangle, whose expression derived from the Law of Sines is described below:

(1)

Where:

- Measure of the line segment FG, in feet.

- Measure of the line segment EG, in feet.

- Measure of the line segment EF, in feet.

- Angle at vertex E, in sexagesimal degrees.

- Angle at vertex F, in sexagesimal degrees.

- Angle at vertex G, in sexagesimal degrees.

We can determine a missing length, by knowing the length of a neighboring side and two consecutive angles. If we know that , and , then the measure of the line segment EF is:

(2)

The length of the line segment EF () is approximately 5 feet.

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