find gh.\nwrite your answer as an integer or as a decimal rounded to the nearest tenth.\ngh =

Explanation:

Step1: Identify triangle type and trigonometric ratio

We have a right - triangle ( \triangle GIH ) with ( \angle I = 90^{\circ} ), ( \angle G=41^{\circ} ), and ( IH = 6 ). We want to find the length of the hypotenuse ( GH ). We can use the sine function, where ( \sin(\theta)=\frac{\text{opposite}}{\text{hypotenuse}} ). For ( \angle G ), the opposite side to ( \angle G ) is ( IH ) and the hypotenuse is ( GH ). So ( \sin(41^{\circ})=\frac{IH}{GH} ).

Step2: Solve for ( GH )

We know that ( IH = 6 ) and ( \sin(41^{\circ})\approx0.6561 ). From ( \sin(41^{\circ})=\frac{6}{GH} ), we can re - arrange the formula to solve for ( GH ): ( GH=\frac{6}{\sin(41^{\circ})} ). Substitute ( \sin(41^{\circ})\approx0.6561 ) into the formula: ( GH=\frac{6}{0.6561}\approx9.1 )

Answer:

( 9.1 )