find de.\nwrite your answer as an integer or as a decimal rounded to the nearest tenth.\nde =
find de.\nwrite your answer as an integer or as a decimal rounded to the nearest tenth.\nde =
Answer
Explanation:
Step1: Identify trigonometric relation
In right - triangle $DEF$ with $\angle D = 22^{\circ}$ and hypotenuse $DF = 8$, and we want to find the adjacent side $DE$ to $\angle D$. We use the cosine function, $\cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}}$. So, $\cos(D)=\frac{DE}{DF}$.
Step2: Substitute values
We know that $D = 22^{\circ}$ and $DF = 8$. Then $DE=DF\times\cos(D)$. $DE = 8\times\cos(22^{\circ})$. Since $\cos(22^{\circ})\approx0.9272$, then $DE = 8\times0.9272=7.4176$.
Step3: Round the result
Rounding $7.4176$ to the nearest tenth gives $7.4$.
Answer:
$7.4$