Question

find: \\(\tan b\\) the figure is not drawn to scale. answer: \\(\frac{11}{60}\\) \\(\frac{11}{60}\\) \\(\frac{60}{11}\\) \\(\frac{60}{11}\\)

Explanation:

Step1: Recall the definition of tangent in a right triangle

In a right triangle, the tangent of an angle is defined as the ratio of the length of the opposite side to the length of the adjacent side. For angle \( B \), we need to identify the opposite and adjacent sides.

Step2: Identify the sides relative to angle \( B \)

• The side opposite to angle \( B \) is \( 640 \) (the side opposite angle \( B \) in the right triangle).
• The side adjacent to angle \( B \) is \( 111 \) (the side next to angle \( B \) that is not the hypotenuse).

Step3: Calculate \( \tan B \)

Using the definition of tangent, \( \tan B=\frac{\text{opposite}}{\text{adjacent}}=\frac{640}{111} \)

Answer:

\(\frac{640}{111}\) (corresponding to the option with \(\frac{640}{111}\))