Help please I needed! Find the missing sides please attach your work!

x = 32

Step-by-step explanation:

Since this is a right triangle, we can use trig functions

sin theta = opp side / hypotenuse

sin 30 = 16/ x

Multiply each side by x

x sin 30 = 16/x * x

x sin 30 = 16

Divide each side by sin 30

x = 16/ sin 30

x = 16 / (1/2)

x = 32

check the picture below.

well, the angle at the vertex d is clearly not a right-angle, let's check for the one at the vertex f which does look like,   however if it's indeed, that means ef is perpendicular to df, in which case their slopes will be negative reciprocal of each other.

so the negative reciprocal of the slope of ef is 1, however the slope of df is not 1, is 1/2, so nope, they're not perpendicular lines.

step-by-step explanation:

here's what happens:

1) the graph of f   = x^2 is shifted 2 units to the right.

2) the resulting graph is reflected in the x-axis, so that the parabola now opens down.

3) this final result is transformed up by 5 units.