Answer:
Answer B: y = 4√3/3, or y = 4/√3
Step-by-step explanation:
Here we have two 30-60-90 triangles, and because of this we know the triangles are similar. Given that the longer hypotenuse is 8 and the angle adjacent to it is 30 degrees, we state that the shorter leg of the larger triangle is determined by
sin 30 degrees = opp / hyp, or sin 30 degrees = opp / 8. Then the shorter leg of the larger triangle (that is, the vertical leg) is 8 sin 30 degrees, or 4.
Now 4 is the length of the longer (vertical) leg of the smaller triangle. In the same way as we found 4 (above), we write:
tan 30 degrees = y / 4, or y = 4 tan 30 degrees, or y = 2.31. This is equivalent to Answer B: y = 4√3/3, or y = 4/√3.
