Answer:
15 unique triangles can be made.
Step-by-step explanation:
Given : A triangle has one angle measures 60° and another angle is an obtuse angle .
To find : How many unique triangles can be made ?
Solution : Since we know, that sum of all three angle of a triangle is 180°
One angle is 60°,
Second angle is obtuse angle(means angle is greater than 90°) then the third angle is acute angle(means less than 90°) .
[tex]60^\circ+O+A=180^\circ[/tex]
[tex]O+A=120^\circ[/tex]
[tex]90^\circ+A+A=120^\circ[/tex]
[tex]A+A=30^\circ[/tex]
This means the third angle is sum of two acute angle is 30°
So, The possible sum is (1+29),(2+28),(3+27),........(15+15)
Therefore, The possible ways the triangle can form is 15 ways.
Hence, 15 unique triangles can be made.
