Question

find gh.
write your answer as an integer or as a decimal rounded to the nearest tenth.
gh =
submit
work it out
not feeling ready yet? these can help:

Explanation:

Step1: Identify triangle type and trigonometric ratio

This is a right - triangle \( \triangle FHG \) with \( \angle H = 90^{\circ} \), \( \angle G=59^{\circ} \), and hypotenuse \( FG = 7 \). We want to find the length of \( GH \), which is adjacent to \( \angle G \). The cosine of an angle in a right - triangle is defined as \( \cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}} \). So, for \( \angle G \), \( \cos(59^{\circ})=\frac{GH}{FG} \).

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

We know that \( FG = 7 \) and \( \theta = 59^{\circ} \). Substituting these values into the cosine formula, we get \( GH=FG\times\cos(59^{\circ}) \).
Using a calculator to find the value of \( \cos(59^{\circ})\approx0.5150 \). Then \( GH = 7\times0.5150 = 3.605 \). Rounding to the nearest tenth, we get \( GH\approx3.6 \).

Answer:

\( 3.6 \)