Question

find the sine, cosine, and tangent of ∠e. simplify your answers and write them as proper fractions, improper fractions, or whole numbers. sin(e) = cos(e) = tan(e) =

Explanation:

Step1: Find the hypotenuse using Pythagorean theorem

Let the hypotenuse $EF = c$, $DE=a = 39$ and $DF = b=80$. By the Pythagorean theorem $c=\sqrt{a^{2}+b^{2}}=\sqrt{39^{2}+80^{2}}=\sqrt{1521 + 6400}=\sqrt{7921}=89$.

Step2: Calculate sine of $\angle E$

The sine of an angle in a right - triangle is defined as $\sin(E)=\frac{\text{opposite}}{\text{hypotenuse}}$. The side opposite $\angle E$ is $DF$. So $\sin(E)=\frac{80}{89}$.

Step3: Calculate cosine of $\angle E$

The cosine of an angle in a right - triangle is defined as $\cos(E)=\frac{\text{adjacent}}{\text{hypotenuse}}$. The side adjacent to $\angle E$ is $DE$. So $\cos(E)=\frac{39}{89}$.

Step4: Calculate tangent of $\angle E$

The tangent of an angle in a right - triangle is defined as $\tan(E)=\frac{\text{opposite}}{\text{adjacent}}$. So $\tan(E)=\frac{80}{39}$.

Answer:

$\sin(E)=\frac{80}{89}$
$\cos(E)=\frac{39}{89}$
$\tan(E)=\frac{80}{39}$