Question

find m∠g.
g e
4
6
f
write your answer as an integer or as a decimal round
m∠g = °
submit

Explanation:

Step1: Identify triangle type and sides

Triangle \( EFG \) is right - angled at \( E \). So, it is a right - triangle. We know that \( GE = 4 \) (adjacent side to \( \angle G \)) and \( EF=6 \) (opposite side to \( \angle G \)).
To find \( \angle G \), we can use the tangent function. The tangent of an angle in a right - triangle is defined as the ratio of the length of the opposite side to the length of the adjacent side. So, \( \tan(\angle G)=\frac{EF}{GE} \)

Step2: Calculate the tangent value

Substitute \( EF = 6 \) and \( GE = 4 \) into the formula for tangent: \( \tan(\angle G)=\frac{6}{4}=\frac{3}{2} = 1.5 \)

Step3: Find the angle

To find \( \angle G \), we take the arctangent (inverse tangent) of \( 1.5 \). Using a calculator, \( \angle G=\arctan(1.5) \)
Calculating \( \arctan(1.5) \approx 56.31^{\circ} \) (rounded to two decimal places)

Answer:

\( 56.31 \) (or if we round to a reasonable decimal place, it can also be presented as per the required precision. If we round to the nearest integer, it is \( 56 \), but the more accurate value from the calculation is approximately \( 56.31 \))