17-42 An isosceles triangle with a vertex angle of $150^{\circ}$, the ratio of the length of the altitude from the vertex to the length of the leg is
(A) $1:(2+\sqrt{3})$.
(B) $1: 3$.
(C) $1: 2$.
(D) $1: \sqrt{3}$.
(6th "Jinyunlin" Junior High School Mathematics Invitational, 1989)
[Solution] As shown in the figure, $b: a=1: 2$. (Note the properties of a $30^{\circ}-60^{\circ}-90^{\circ}$ right triangle) Therefore, the correct choice is $(C)$.