Respuesta :

Answer:

Step-by-step explanation:

Triangle ABC is a right angle triangle.

From the given right angle triangle,

AB represents the hypotenuse of the right angle triangle.

With m∠A as the reference angle,

AC represents the adjacent side of the right angle triangle.

BC represents the opposite side of the right angle triangle.

To determine tan m∠A, we would apply the tangent trigonometric ratio.

Tan θ = opposite side/adjacent side. Therefore,

Tan A = √32/2 = (√16 × √2)/2

Tan A = (4√2)/2

Tan A = 2√2

The value of tan A is in the simplest radical form  [tex]2\sqrt{2}[/tex].

We have to determine

The exact value of tanA in the simplest radical form.

According to the question,

The value of tan A is determined by using the formula;

The tangent is equal to the length of the side opposite the angle divided by the length of the adjacent side.

[tex]\rm TanA = \dfrac{Perendicular}{Base}\\\\[/tex]

Where Perpendicular = [tex]\sqrt{32}[/tex] and Base = 2

Substitute all the values in the formula;

[tex]\rm TanA = \dfrac{Perendicular}{Base}\\\\TanA = \dfrac{\sqrt{32}}{2}\\\\TanA = \dfrac{4}{\sqrt{2}} \times \dfrac{\sqrt{2}}{\sqrt{2}}\\\\TanA = 2\sqrt{2}[/tex]

Hence, The value of tan A is [tex]2\sqrt{2}[/tex].

To know more about Tangent click the link given below.

https://brainly.com/question/13710437

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