In DABC, what could the 7 shown in the ratio sin A = 7/9 represent?
A) the length of the adjacent side of angle B
B) the length of the opposite side of angle A
C) the length of the hypotenuse of a right triangle
D) the length of the adjacent side of angle A
I did this as an acute angle with A at the top, i got A for my answer
If triangle ABC is right-triangle right angled at B or C, then
by the definition of sin(A), it is the opposite side length divided by the hypotenuse.
To determine the meaning of the number 7 in the ratio sin A = 7/9 in triangle DABC, we need to understand what the sine function represents in a right triangle.
The sine of an angle in a right triangle is defined as the ratio of the length of the side opposite to that angle to the length of the hypotenuse. So, in the given ratio sin A = 7/9, the numerator (7) represents the length of the side opposite to angle A, and the denominator (9) represents the length of the hypotenuse of the right triangle.
Therefore, in this specific case, the number 7 represents the length of the side opposite to angle A.
Looking at the answer choices provided:
A) the length of the adjacent side of angle B: This is not the correct interpretation of the number 7 in the ratio.
B) the length of the opposite side of angle A: This is the correct interpretation because the sine function represents the ratio of the opposite side to the hypotenuse.
C) the length of the hypotenuse of a right triangle: This is not the correct interpretation, as the denominator represents the length of the hypotenuse.
D) the length of the adjacent side of angle A: This is not the correct interpretation, as the number 7 represents the length of the side opposite to angle A, not the adjacent side.
Therefore, the correct answer is B) the length of the opposite side of angle A.