Question

find the tangent of \\( \angle d \\).
simplify your answer and write it as a proper fraction, improper fraction, or whole number.
\\( \tan (d)= \\)

Explanation:

Step1: Find the length of \(BC\)

Use the Pythagorean theorem \(a^{2}+b^{2}=c^{2}\). Here \(c = 53\), \(a=28\), and \(b = BC\). So \(BC=\sqrt{53^{2}-28^{2}}=\sqrt{(53 + 28)(53 - 28)}=\sqrt{81\times25}=45\).

Step2: Recall the tangent formula

For a right - triangle, \(\tan\theta=\frac{\text{opposite}}{\text{adjacent}}\). For \(\angle D\), the opposite side is \(BC\) and the adjacent side is \(CD\).
So \(\tan(D)=\frac{BC}{CD}\).

Step3: Substitute the values

Since \(BC = 45\) and \(CD=28\), \(\tan(D)=\frac{45}{28}\).

Answer:

\(\frac{45}{28}\)