Question

I’ve already answered Part A. Part B & C have the same drop down answers choices.

Answer 1

Given

$\begin{gathered} \tan (12)=\frac{x}{6} \\ \tan (78)=\frac{6}{x} \end{gathered}$

To check whether the value of x is found using both equation:

It is known that,

$\tan \theta=\frac{oppositeside}{\text{adjacent side}}$

From the given figure, it is clear that the angles of the triangle ABC,

$\begin{gathered} \angle A=90,\angle C=12 \\ \angle B=180-(\angle A+\angle C) \\ =180-(90+12) \\ =78 \end{gathered}$

Therefore for the angle C=12 degree,

The equation can be written as,

$\tan \theta=\frac{x}{6}$

Since x is the opposite side and 6 is the adjacent side.

However for angle B. the opposite side will be 6 and the adjacent side will be x.

Thus, we get

$\tan \theta=\frac{6}{x}$

Hence, Andre and Mia both are correct.