Question

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

Explanation:

Step1: Find the length of \(DC\)

Use the Pythagorean theorem \(a^{2}+b^{2}=c^{2}\). Here, \(c = 74\), \(b = 70\), and \(a=DC\).

$$
LATEXBLOCK0
$$

Step2: Calculate \(\sin(D)\)

\(\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}\). For \(\angle D\), the opposite side to \(\angle D\) is \(EC = 70\), and the hypotenuse is \(DE=74\).
\(\sin(D)=\frac{70}{74}=\frac{35}{37}\)

Step3: Calculate \(\cos(D)\)

\(\cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}}\). For \(\angle D\), the adjacent side to \(\angle D\) is \(DC = 24\), and the hypotenuse is \(DE = 74\).
\(\cos(D)=\frac{24}{74}=\frac{12}{37}\)

Step4: Calculate \(\tan(D)\)

\(\tan\theta=\frac{\text{opposite}}{\text{adjacent}}\). For \(\angle D\), the opposite side to \(\angle D\) is \(EC = 70\), and the adjacent side is \(DC=24\).
\(\tan(D)=\frac{70}{24}=\frac{35}{12}\)

Answer:

\(\sin(D)=\frac{35}{37}\), \(\cos(D)=\frac{12}{37}\), \(\tan(D)=\frac{35}{12}\)