Question

find tan(β) in the triangle. answer:

Explanation:

Step1: Recall the definition of tangent

In a right triangle, the tangent of an angle is the ratio of the length of the opposite side to the length of the adjacent side. For angle \(\beta\) in right triangle \(ABC\) (right - angled at \(C\)), \(\tan(\beta)=\frac{\text{opposite side to } \beta}{\text{adjacent side to } \beta}\)

Step2: Identify the opposite and adjacent sides

The side opposite to angle \(\beta\) is \(AC = 8\), and the side adjacent to angle \(\beta\) is \(BC=15\) (since \(BC\) is one of the legs forming angle \(\beta\) and \(AC\) is the other leg opposite to \(\beta\) in the right - triangle at \(C\)).

Step3: Calculate \(\tan(\beta)\)

Using the formula \(\tan(\beta)=\frac{\text{opposite}}{\text{adjacent}}\), we substitute the values of the opposite and adjacent sides. So \(\tan(\beta)=\frac{AC}{BC}=\frac{8}{15}\)

Answer:

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