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 \( \triangle IHG \) with \( \angle I = 90^\circ \), \( HI = 6.5 \) (opposite to \( \angle G \)), and hypotenuse \( HG = 7.2 \). We use the sine ratio: \( \sin(\angle G)=\frac{\text{opposite}}{\text{hypotenuse}}=\frac{HI}{HG} \).

Step2: Calculate the sine value

Substitute the values: \( \sin(\angle G)=\frac{6.5}{7.2}\approx0.9028 \).

Step3: Find the angle

Take the inverse sine: \( \angle G=\sin^{-1}(0.9028) \). Using a calculator, \( \angle G\approx64.5^\circ \) (rounded to the nearest tenth).

Answer:

\( 64.5 \)