Question

find gi.
triangle image with right angle at h, gh=2, angle at i is 34°
write your answer as an integer or as a decimal rounded to the nearest tenth.
gi =
submit
work it out
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Explanation:

Step1: Identify triangle type and trigonometric ratio

We have a right - triangle \( \triangle GHI \) with \( \angle H = 90^{\circ} \), \( \angle I=34^{\circ} \), and \( GH = 2 \). We want to find the length of the hypotenuse \( GI \). We can use the sine function, where \( \sin(\theta)=\frac{\text{opposite}}{\text{hypotenuse}} \). In this case, for angle \( I \), the opposite side to \( \angle I \) is \( GH \) and the hypotenuse is \( GI \). So \( \sin(34^{\circ})=\frac{GH}{GI} \).

Step2: Solve for \( GI \)

We know that \( GH = 2 \) and \( \sin(34^{\circ})\approx0.5592 \). From \( \sin(34^{\circ})=\frac{2}{GI} \), we can re - arrange the formula to solve for \( GI \): \( GI=\frac{2}{\sin(34^{\circ})} \).

Substitute the value of \( \sin(34^{\circ}) \) into the formula: \( GI=\frac{2}{0.5592}\approx3.6 \)

Answer:

\( 3.6 \)