Find the missing lengths. plz math is not my subject

For the figure on the left, the answers are a = 8 and b = 4

This is a 30-60-90 triangle. The short leg is always opposite the smallest angle (30 degrees). The rule is the smallest side is opposite the smallest angle. Similarly, the largest side is opposite the largest angle. In a right triangle the largest side is always opposite the 90 degree angle. This side is the hypotenuse.

Recall that the longer leg is sqrt(3) times the short leg. The notation "sqrt" is shorthand for "square root".

So long leg = (short leg)*sqrt(3) which means b = 4 must be the case to end up with long leg = 4*sqrt(3)

The hypotenuse is twice that of the short leg, so a = 2*b = 2*4 = 8

For the figure on the right, the answers are x = 2*sqrt(3) and y = 2

The short leg is y, which is opposite the 30 degree angle (this is another 30-60-90 triangle). So y is half of the hypotenuse 4. That explains how y = 2.

The long leg x is equal to sqrt(3) times the short leg, so

(long leg) = (short leg)*sqrt(3)

x = y*sqrt(3)

x = 2*sqrt(3)

560

step-by-step explanation:

giggidy

36 girls

step-by-step explanation:

the 48 boys is 4 parts of the ratio

divide 48 by 4 to obtain one part of the ratio

= 12 ← 1 part of the ratio

3 parts = 3 × 12 = 36 ← number of girls