Answer:
A
Step-by-step explanation:
law of sine
c/sin(C) = b/sin(B) = a/sin(A)
with the sides and corresponding angles being always opposite.
sin(90) = 1
sin(30) = 0.5
c, the Hypotenuse, is the longest side in such a right-angled triangle.
c/1 = b/0.5
b = c×0.5 = c/2
so, one side has to be half the length of the longest side (Hypotenuse).
the only answer meeting that criteria is A.
the longest side is 10×sqrt(3) = 17.32...
the side half of that is 5×sqrt(3).
and Pythagoras for such a triangle is then
c² = (c/2)² + a²
c² = c²/4 + a²
so, a² = 3c²/4
c² = c²/4 + 3c²/4
therefore we can check also the third side
15² = 3×(5×sqrt(3))² = 3×25×3 = 3×75 = 225 = 15²
correct.
A is such a triangle.
