Determine whether the following statement is true or false. Justify your answer.
1 answer:
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 = .
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."
You might be interested in
Answer:
Step-by-step explanation:
In the given figure, PQRS is a rhombus and SRM is an equilateral triangle.
We are also given that SN⊥RM and that ∠PRS = 55°.
And we want to find the measure of ∠QSN.
Remember that since PQRS is a rhombus, the angles formed by its diagonals are right angles. Let the intersection point of the diagonals be K. Therefore:
Now, RKS is also a triangle. The interior angles of all triangles must be 180. Thus:
Substitute in known values:
Solve for ∠KSR:
Since SRM is an equilateral triangle, this means that:
Note that RNS is also a triangle. Therefore:
Substitute in known values:
So:
∠QSN is the addition of the two angles:
Therefore: