Question

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

Explanation:

Step1: Find the length of \(CD\)

Use the Pythagorean theorem \(a^{2}+b^{2}=c^{2}\). Here \(c = 17\), \(b = 8\), and \(a=CD\). So \(CD=\sqrt{17^{2}-8^{2}}=\sqrt{(17 + 8)(17 - 8)}=\sqrt{25\times9}=\sqrt{225}=15\).

Step2: Calculate \(\tan(B)\)

The formula for \(\tan\) in a right - triangle is \(\tan\theta=\frac{\text{opposite}}{\text{adjacent}}\). For \(\angle B\), the opposite side is \(CD = 15\) and the adjacent side is \(BD = 8\). So \(\tan(B)=\frac{CD}{BD}\).

Answer:

\(\frac{15}{8}\)