Q:

Two sides of a triangle measure 5 cm and 9 cm. It has an angle that measures 128°. Which type of triangle could it be? Select all that apply. A. acute isoceles B. obtuse scalene C. obtuse equilateral D. obtuse isosceles E. acute scalene F. obtuse right

Accepted Solution

A:
An obtuse triangle has one angle with more than 90 degrees. since one angle has 128º, the triangle must be obtuse.
An equilateral triangle has all internal angles equal to 60 degrees, so there's no such thing as an "obtuse equilateral" triangle.
For it to be isosceles, it must have 2 equal sides, since 9>5, it must be as the picture suggests.
so the base must be 9 cm, and the green line, half of the base must be 4,5cm. The angles in the bottom should be (180-128)/2=26º
as such the green line length is 5*COS(26)=4,49 which is close to 4.50
it is a plausible result then.
As an alternative, of course, all of the sides could be different from each other, making it scalene
options B) and D) are correct, all others are false