Question

find: tan b
right triangle with right angle, vertical leg 60, horizontal leg 32, hypotenuse 68, angle b at top vertex, angle a at bottom-right vertex
the figure is not drawn to scale
answer
options:
\\(\frac{32}{60}\\), \\(\frac{60}{32}\\), \\(\frac{32}{68}\\), \\(\frac{60}{68}\\)

Explanation:

Step1: Recall the definition of tangent in a right triangle

In a right triangle, the tangent of an acute 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 \( B \)

In the given right triangle, the right angle is at the vertex between the sides of length 60 and 32. For angle \( B \):

• The opposite side (opposite to angle \( B \)) is the side with length 32 (since it is across from angle \( B \)).
• The adjacent side (adjacent to angle \( B \)) is the side with length 60 (since it forms angle \( B \) along with the hypotenuse).

Step3: Calculate \( \tan B \)

Using the definition of tangent, \( \tan B=\frac{\text{opposite}}{\text{adjacent}} \). Substituting the lengths of the opposite and adjacent sides, we get \( \tan B = \frac{32}{60} \).

Answer:

\(\frac{32}{60}\) (corresponding to the first option: \(\frac{32}{60}\))