Answer:
The right answer is the second option, 89,91.
Step-by-step explanation:
Let's say hypotenuse is x. Then:
sin(30º) = 0,5.
sinθ = [tex]\frac{y}{x}[/tex]
[tex]\frac{1}{2} = \frac{19}{x} \\ x = 38[/tex]
Let's say another cathet is z. Then:
[tex]x^2 = y^2+z^2\\ z = \sqrt{x^2-y^2} \\ z = \sqrt{38^2-19^2} \\ z= \sqrt{(38-19)(38+19)} \\ z = \sqrt{19*57} \\ z = \sqrt{1083}[/tex]
[tex]P = x+y+z \\ P = 19+38+ \sqrt{1083} \\ P = 57+\sqrt{1083}[/tex]
[tex]\sqrt{1083} = 32,908... = 32,91[/tex]
[tex]P = 57 + 32,91 = 89,91[/tex]
