Answer: The given statement is FALSE.
Step-by-step explanation: We are given to check whether he following statement is true or false :
"The sine of an angle in a right triangle is equal to the ratio of the length of the side adjacent to the angle divided by the length of the hypotenuse. "
Let us consider the right-angled triangle ABC as shown in the attached figure below.
With respect to acute angle C, we can see that
perpendicular, p = AB
base, b = BC
and
hypotenuse, h = AC.
We know that
sine of an angle in a right-angled triangle is equal to the ratio of the perpendicular to the base.
So, we must have
[tex]\sin \angle C=\dfrac{p}{h}\\\\\\\Rightarrow \sin \angle C=\dfrac{AB}{AC}.[/tex]
Since AB is the opposite side to angle C, not adjacent, therefore
sine of any angle in a right-angled triangle is the ratio of the length of the OPPOSITE SIDE to length of the hypotenuse.
Thus, the given statement is FALSE.
