Question

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

Answer 1

The value of g across from angle G is 5feet

According to sine rule

$\frac{e}{sinE}=\frac{f}{sinF}=\frac{g}{sinG}$

Given the following

∠G = 45°

∠F = 82°

f = 7feet

Required

side g

Substitute the given values into the formula

$\frac{f}{sinF}=\frac{g}{sinG}\\ \frac{7}{sin82}=\frac{g}{sin45}\\\frac{7}{0.9903}=\frac{g}{0.7071}\\7.0686=\frac{g}{0.7071}\\g=7.0686*0.7071\\g=4.998\\g\approx5ft$

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

Learn more here: brainly.com/question/15018190

Answer 2

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

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

$\frac{e}{\sin E} = \frac{f}{\sin F} = \frac{g}{\sin G}$ (1)

Where:

$e$ - Measure of the line segment FG, in feet.

$f$ - Measure of the line segment EG, in feet.

$g$ - Measure of the line segment EF, in feet.

$E$ - Angle at vertex E, in sexagesimal degrees.

$F$ - Angle at vertex F, in sexagesimal degrees.

$G$ - 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 $f = 7\,ft$, $G = 45^{\circ}$ and $F = 82^{\circ}$, then the measure of the line segment EF is:

$g = f\cdot \left(\frac{\sin G}{\sin F} \right)$ (2)

$g = (7\,ft)\cdot \left(\frac{\sin 45^{\circ}}{\sin 82^{\circ}} \right)$

$g\approx 4.998\,ft$

$g \approx 5\,ft$

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