Question

question in \\(\triangle efg\\), the measure of \\(\angle g = 90^\circ\\), \\(gf = 15\\), \\(eg = 8\\), and \\(fe = 17\\). what is the value of the cosine of \\(\angle e\\) to the nearest hundredth?

Explanation:

Step1: Recall cosine definition

In a right triangle, $\cos(\theta) = \frac{\text{adjacent}}{\text{hypotenuse}}$ for an acute angle $\theta$.

Step2: Identify sides for $\angle E$

In $\triangle EFG$ with $\angle G = 90^\circ$, for $\angle E$:

• Adjacent side to $\angle E$ is $EG = 8$.
• Hypotenuse is $FE = 17$.

Step3: Calculate $\cos(\angle E)$

$\cos(\angle E) = \frac{EG}{FE} = \frac{8}{17}$

Step4: Compute the value

$\frac{8}{17} \approx 0.470588$

Step5: Round to nearest hundredth

Rounding $0.470588$ to the nearest hundredth gives $0.47$.

Answer:

$0.47$