Question

Andre and Mai are discussing how to solve for side AB. Andre thinks he can

use the equation tan(12 degrees)=x/6 to solve for AB. Mai thinks she can use
the equation tan(78 degrees)=6/x to solve for AB. Do you agree with either of
them? Show or explain your reasoning.

Answer 1

Both Andre and Mai are correct

Explanation:

A drawing of the the triangle ΔABC is created with MS Visio and attached here

In the drawing, we have;

Segment AB = x

Segment AC = 6

By trigonometric ratio, in a right triangle we have;

`Tan(\angle X) = (The \ length \ of \ the \ opposite \, side \ to \ \angle X )/(The \ length \ of \ the \ adjacent\, side \ to \ \angle X)`

Where 'X' = 12° as shown in the figure, we have;

`tan(12 ^(\circ)) = (AB)/(BC) = (x)/(6)`

Therefore, Andre is correct

Similarly, we have;

`tan(78 ^(\circ)) = (BC)/(AB) = (6)/(x)`

Therefore, Mai is also correct

Therefore, Andre and Mai are correct.