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
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
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.