Question

find gi.
triangle image with right angle at i, side gh = 7, angle at g is 25°
write your answer as an integer or as a decimal rounded to the nearest tenth.
gi =
submit

Explanation:

Step1: Identify triangle type and trigonometric ratio

We have a right - triangle \( \triangle GIH \) with \( \angle I = 90^{\circ} \), \( GH = 7 \), and \( \angle G=25^{\circ} \). We want to find the length of \( GI \). In a right - triangle, the cosine of an angle is defined as the adjacent side divided by the hypotenuse. For \( \angle G \), the adjacent side is \( GI \) and the hypotenuse is \( GH \). So, \( \cos(G)=\frac{GI}{GH} \).

Step2: Substitute values and solve for \( GI \)

We know that \( \cos(25^{\circ})\approx0.9063 \) and \( GH = 7 \). From the formula \( \cos(G)=\frac{GI}{GH} \), we can re - arrange it to \( GI = GH\times\cos(G) \). Substituting the values, we get \( GI=7\times\cos(25^{\circ}) \).
\( GI = 7\times0.9063\approx6.3441 \). Rounding to the nearest tenth, we get \( GI\approx6.3 \).

Answer:

\( 6.3 \)