Question

Determine whether the following statement is true or false. Justify your answer.

Answer 1

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 = $\frac{opp}{adj}$.

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."