Question

32 m, 25 m, 20 m. which ratio represents the tangent of the marked angle in the diagram? a. $\frac{4}{5}$ b. $\frac{5}{4}$ c. $\frac{5}{8}$ d. $\frac{25}{32}$

Explanation:

Step1: Recall tangent definition

In a right triangle, the tangent of an acute angle is the ratio of the length of the opposite side to the length of the adjacent side.

Step2: Identify sides for marked angle

For the marked angle, the opposite side (to the angle) has length 25 m, and the adjacent side (to the angle) has length 20 m.

Step3: Calculate tangent ratio

Tangent of the marked angle = $\frac{\text{opposite}}{\text{adjacent}} = \frac{25}{20}$
Simplify $\frac{25}{20}$ by dividing numerator and denominator by 5: $\frac{25\div5}{20\div5} = \frac{5}{4}$

Answer:

B. $\frac{5}{4}$