Question

question
find the value of \\( \cos e \\) rounded to the nearest hundredth, if necessary.
(image of a right triangle \\( \triangle gfe \\) with right angle at \\( f \\), \\( gf = 8 \\), \\( fe = 15 \\))

Explanation:

Step1: Identify triangle type

It's a right - triangle at \( F \), so we can use Pythagorean theorem to find the hypotenuse \( GE \). The Pythagorean theorem is \( c^{2}=a^{2}+b^{2} \), where \( a = 8 \), \( b = 15 \). So \( GE=\sqrt{8^{2}+15^{2}}=\sqrt{64 + 225}=\sqrt{289}=17 \).

Step2: Recall cosine definition

For angle \( E \) in right - triangle \( \triangle FGE \), \( \cos E=\frac{\text{adjacent side to }E}{\text{hypotenuse}} \). The adjacent side to angle \( E \) is \( FE = 15 \), and the hypotenuse \( GE = 17 \). So \( \cos E=\frac{15}{17}\approx0.88235\).

Step3: Round to hundredth

Rounding \( 0.88235 \) to the nearest hundredth, we look at the thousandth digit which is \( 2 \). Since \( 2<5 \), we keep the hundredth digit as it is. So \( \cos E\approx0.88 \).

Answer:

\( 0.88 \)