If we say that side "a" is the shortest (adjacent), side "b" is the second shortest (opposite), and side "c" is the longest (hypotenuse): then angle A would be 30°, angle B would be 60°, and angle C would be 90°
tan B = b/a
or
a tan B = b
they have 4 as the smallest value in all four options, so we know that a=4
4 tan 60° = b
tan 60° = √3
so, 4 tan 60° = 4√3
b=4√3
that leaves two options left, so now we find "c":
c^2 = (a^2) + (b^2)
OR
[tex]c= \sqrt{a^{2} + b^{2}} [/tex]
[tex]c= \sqrt{4^{2}+(4\sqrt{3})^{2}} [/tex]
[tex]c= \sqrt{16+48} \\ c=\sqrt{64} \\ c=8 [/tex]
so a=4, b=4√3, and c=8
Making your answer B
