Question

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.

Answer 1

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

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 =
`(opp)/(adj)`.

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."