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Determine whether the following statement is true or false. Justify your answer.
If O is an angle in any triangle, then tan 0 is the length of the side opposite O divided by the length of the
side adjacent to 0.
Choose the correct answer below.
OA. The statement is false. tan 0 is always equal to the length of the side opposite o divided by the
length of the length of the hypotenuse.
OB. The statement is false. This is true only if O is an acute angle in a right triangle.
O C. The statement is false. This is true only if O is an obtuse angle in a right triangle.
OD. The statement is true, tan 0 is always equal to the length of the side opposite o divided by the
length of the side adjacent to 0.

Determine whether the following statement is true or false Justify your answer If O is an angle in any triangle then tan 0 is the length of the side opposite O class=

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Answer:

B. The statement is false. This is true only if θ is an acute angle in a right triangle.

Step-by-step explanation:

Trigonometric ratio formula can only be applied to define the relationship between the angles of a right triangle and its side lengths.

Therefore, it is impossible to define or find the tan θ of "any triangle". It only applies to right angled triangles.

In the case of a right triangle, given a reference angle, θ, tan θ = side lenght opposite to θ ÷ side lenght adjacent to θ (tan θ = [tex] \frac{opp}{adj} [/tex].

A right triangle has two acute angles and 1 right angle that which is 90°.

Therefore, we can conclude that:

"B. The statement is false. This is true only if θ is an acute angle in a right triangle."

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