Question

(SAT Prep) In △ABC AC⊥BC , m∠B = 30° , and M is a point on side AB , such that m∠AMC = 105°. Which of the following segments has the shortest length? A. AC B. BC C. AM D. MB
Please answer in a statement reason format-give explanations
Thanks

Answer 1

In ΔABC:

AC is the shortest side as it's opposite to the smallest angle

in Δ AMC:

AM is the smallest as it's opposite to the smallest angle

also, AM is smaller than AC

leaving us with two sides: AM and BM

BM = BC as it's an isosceles triangle

so AM is the shortest