find fg.\nwrite your answer as an integer or as a decimal rounded to the nearest tenth.\nfg = \nsubmit
find fg.\nwrite your answer as an integer or as a decimal rounded to the nearest tenth.\nfg = \nsubmit
Answer
Explanation:
Step1: Identify triangle type and trigonometric ratio
We have a right - triangle (FGH) with (\angle F = 39^{\circ}), (\angle G=90^{\circ}), and (GH = \sqrt{86}\approx9.27). We want to find (FG). We can use the tangent function, since (\tan\theta=\frac{\text{opposite}}{\text{adjacent}}). In (\triangle FGH), (\tan(\angle F)=\frac{GH}{FG}).
Step2: Rearrange the formula to solve for FG
From (\tan(39^{\circ})=\frac{GH}{FG}), we can rearrange it to (FG=\frac{GH}{\tan(39^{\circ})}). We know that (GH = \sqrt{86}\approx9.27) and (\tan(39^{\circ})\approx0.8098).
Step3: Calculate FG
Substitute the values into the formula: (FG=\frac{\sqrt{86}}{\tan(39^{\circ})}\approx\frac{9.27}{0.8098}\approx11.4) (rounded to the nearest tenth).
Answer:
(11.4)