Question

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

Explanation:

Step1: Find the length of BC

In right triangle \(DBC\), by the Pythagorean theorem \(a^{2}+b^{2}=c^{2}\), where \(c = 34\) (hypotenuse), \(DB = 30\) (one leg), and \(BC\) is the other leg. So \(BC=\sqrt{34^{2}-30^{2}}\). Calculate \(34^{2}=1156\) and \(30^{2} = 900\), then \(BC=\sqrt{1156 - 900}=\sqrt{256}=16\).

Step2: Calculate \(\tan(C)\)

In a right triangle, \(\tan(\theta)=\frac{\text{opposite}}{\text{adjacent}}\). For \(\angle C\), the opposite side is \(DB = 30\) and the adjacent side is \(BC = 16\). So \(\tan(C)=\frac{DB}{BC}=\frac{30}{16}\), simplify it by dividing numerator and denominator by 2, we get \(\frac{15}{8}\).

Answer:

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