Which dimensions can create only one unique triangle? a. three angles measuring 25,65,and 90 b. three angles measuring 50,50,and 50 c. three sides measuring 5 in,12 in, and 14 in d. three sides measuring 4 ft,8 ft, and 14 ft

Verify each case

case A. Three angles measuring 25,65,and 90

sum of a internal angles=25+65+90> 180° is ok

That dimensions can create infinity similar triangles

case B. Three angles measuring 50,50,and 50

sum of a internal angles=50+50+50> 150°  is not a triangle

therefore

That dimensions cannot create a triangle

case C. Three sides measuring 5 in,12 in,and 14 in

Applying the Triangle Inequality Theorem

5+12>14 -- >  is ok

14+5>12 --- > is ok

12+14>5 --- > is ok

That dimensions can create only one unique triangle

case  D. Three sides measuring 4 ft,8 ft, and 14 ft

Applying the Triangle Inequality Theorem

4+8>14 -- >  is not true

therefore

That dimensions cannot create a triangle

the answer is

Option C. Three sides measuring 5 in,12 in,and 14 in

probability for j is 1/4

while

a is 1/6