Question

30 pointss!HELP! Two students get into an argument about the correct answer.

Rhianna states that the correct trig function is tan A = 3/4. Christopher insists that the correct trig function is tan C = 4/3. Who is correct? In writing your response, be sure to include the terms opposite side, adjacent side, tangent ratio, and reference angle. Be sure to restate the question and explain your position with at least four sentences.

Answer 1

Both Rhianna and Christopher were correct as they took different reference angles.

Explanation:

Step 1:

`tan \theta = (opposite side)/(adjacentside) .`

The value of the tan of a reference angle is calculated using the above formula.

The hypotenuse is the longest side of the triangle is always opposite the right angle of the triangle.

In this triangle, the hypotenuse is the side measuring 5 units.

Step 2:

When the reference angle is A, the opposite side measures 3 units and the adjacent side measures 4 units.

So
`tan A = (3)/(4) .`

When the reference angle is C, the opposite side measures 4 units and the adjacent side measures 3 units.

So
`tan C = (4)/(3) .`

So both Rhianna and Christopher were right as they took different reference angles i.e. A and C.