Question

find ( mangle g ).

write your answer as an integer or as a decimal rounded to the nearest tenth.
( mangle g = square^circ )

Explanation:

Step1: Identify triangle type and trigonometric ratio

We have a right - triangle \( \triangle FHG \) with \( \angle F = 90^{\circ} \), \( FH = 6.8 \), and \( FG=4.1 \). We want to find \( m\angle G \). The tangent of an angle in a right - triangle is defined as the ratio of the opposite side to the adjacent side. For \( \angle G \), the opposite side is \( FH \) and the adjacent side is \( FG \). So, \( \tan(\angle G)=\frac{FH}{FG} \)

Step2: Substitute the values and calculate the angle

Substitute \( FH = 6.8 \) and \( FG = 4.1 \) into the tangent formula: \( \tan(\angle G)=\frac{6.8}{4.1}\approx1.6585 \)

To find \( \angle G \), we take the inverse tangent (arctangent) of \( 1.6585 \). So, \( \angle G=\arctan(1.6585) \)

Using a calculator (make sure the calculator is in degree mode), we find that \( \arctan(1.6585)\approx58.9^{\circ} \)

Answer:

\( 58.9 \)