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:
Given: Two sides of a triangles measure 5 cm and 9 cm.  
An angle measure of the triangle is 128 degrees.  
Since 128 degrees is greater than 90 degrees and less than 180 degrees, the triangle is obtuse. Therefore option A) acute isosceles and option E) acute scalene does not apply.  
option F) obtuse right is also not possible, as the sum of angles of a triangle is 180 degrees, the sum of the other two angles is 180-128=52 degrees. Therefore, none of the other two angles could be 90 degrees.  
option C) Obtuse equilateral is not possible because, in an equilateral triangle all angles are 60 degrees.  
In a scalene triangle, all angles and all sides are different. Therefore, the triangle could be Option B) obtuse scalene   
In a scalene triangle, two angles and the sides opposite to them are equal. since we only know the measures of two sides of the triangle, it could be Option D) Obtuse isosceles.   
So, the answer is: It could be option B) Obtuse Scalene or option D) Obtuse isosceles.