Question

use triangle abc to answer questions 1–2.

1. which side is opposite <c.
2. what is tan a?

Explanation:

Question 1

In a triangle, the side opposite an angle is the side that does not form the angle. For $\angle C$ in triangle $ABC$, the sides forming $\angle C$ are $BC$ and $AC$. So the side opposite $\angle C$ is $AB$.

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 $\angle A$, the opposite side to $\angle A$ is $BC$ (length 3 in) and the adjacent side is $AB$ (length 4 in).

Step2: Calculate $\tan A$

Using the formula $\tan A=\frac{\text{opposite}}{\text{adjacent}}$, we substitute the lengths: $\tan A = \frac{BC}{AB}=\frac{3}{4}$.

Answer:

$AB$ (or the side with length 4 in)

Question 2