Question

The length of segment AB is 9 mm.

Triangle A B C is shown. Angle A B C is a right angle. Angle B A C is 60 degrees and angle A C B is 30 degrees. The length of A B is 9 millimeters.

Which statements regarding triangle ABC are correct? Check all that apply.

AB is the shortest segment in △ABC.
BC = 18mm
AC = 2AB
AC = 9 StartRoot 3 EndRoot
BC is the longest segment in △ABC

Answer 1

Correct statements:
- AB is the shortest segment in △ABC. (AB is opposite the smallest angle, 30°.)
- AC = 2AB. (In a 30°-60°-90° triangle the hypotenuse = 2 × side opposite 30°; so AC = 2·9 = 18 mm.)

Incorrect statements:
- BC = 18 mm. (BC = 9√3 mm ≈ 15.59 mm.)
- AC = 9√3. (AC = 18 mm.)
- BC is the longest segment in △ABC. (AC, the hypotenuse, is longest.)