1 - AB is the Hypotenuse, BC is the opposite, AC is the adjacent (next to)
AB is the Hypotenuse because it is across from the right angle. BC is the opposite because its on the opposite side of the angle. AC is next to (adjacent) of the angle.
2 - the ratio is 30/1 = 5/b
This is because S O/H C A/H T O/A or Sohcahtoa.
S is the sine, which is Opposite over Hypotenuse. C is the cosine, which is Adjacent over Hypotenuse, and T is tangent which is Opposite over Adjacent. So look at what we labeled, we need to find the adjacent side, or b, and we have the opposite side, 5. So what has opposite and adjacent? Tangent.
So we do tan(30)/1 = 5/b, and cross multiply.
Now the last question. Hypotenuse is always C. But the other two values don’t matter where you put them on the left side since its multiplication. So its 7.7^2 * 6^2 = c^2 which is 59.29 * 36 = C^2. 2134.44 = c^2. Square root sides so it is 46.2 = c. The answer is 46.2
.