Question

Which ratio represents sin A? a) 8/17 b) 15/17 c) 17/15 d) 17/8

Answer 1

the picture in the attached figure

we know that
in the right triangle ABD
AB²=BD²+AD²-----> BD²=AB²-AD²
AB=8
AD=64/17
BD²=8²-(64/17)²----> 64-(4096/289)----> BD²=14400/289
BD=√(14400/289)-----> BD=120/17

sin A=BD/AB-----> sin A=(120/17)/8----> 15/17

the answer is
15/17

Answer 2

Answer:

b) 15/17

Step-by-step explanation:

Notice that ΔABD is a right triangle with AB the hypotensue. The sine of an angle is the ratio of

opposite leg

hypotenuse

. In ΔABD you can solve for the opposite leg (BD) using the Pythagorean Theorem.

BD2 + [64/17)2 = 82

BD =

120

17

. Therefore, sin A =

15

17