find the sine, cosine, and tangent of $angle d$.\nsimplify your answers and write them as proper fractions…

Explanation:

Step1: Calculate hypotenuse $ED$

Use Pythagorean theorem: $$ED = \sqrt{DF^2 + EF^2} = \sqrt{8^2 + 15^2} = \sqrt{64 + 225} = \sqrt{289} = 17$$

Step2: Find $\sin(D)$

Opposite over hypotenuse: $$\sin(D) = \frac{EF}{ED} = \frac{15}{17}$$

Step3: Find $\cos(D)$

Adjacent over hypotenuse: $$\cos(D) = \frac{DF}{ED} = \frac{8}{17}$$

Step4: Find $\tan(D)$

Opposite over adjacent: $$\tan(D) = \frac{EF}{DF} = \frac{15}{8}$$

Answer:

$\sin(D) = \frac{15}{17}$ $\cos(D) = \frac{8}{17}$ $\tan(D) = \frac{15}{8}$