how many distinct Triangles ABC are there two similarity such that the magnitudes of angle A B and C in degree are positive integers and satisfy
Answers
Answer:
2700 Triangles
Step-by-step explanation:
how many distinct Triangles ABC are there two similarity such that the magnitudes of angle A B and C in degree are positive integers
Possible Angles
Angle A = 1 B & C could take 89 Values (1 + 178 , 89 + 90)
A = 2 B & C could take 89 Values (1 + 177 ,......................89 + 178)
but 2 , 1 , 177 is already in 1 , 2 , 177
A= 2 88 Values
A = 3 B & could take 88 Values (1 + 176 , .....88+ 89) - 2 Values already taken in 1st two cases
88 - 2 = 86 Values
A = 4 = 88 - 3 = 85 Values
A =5 87-4 = 83
A=59 60 - 58 = 2 Values
A = 60 60 - 59 = 1 Value
This way 89 + 88 + 86 + 85 + 83 + 82 +.......................... 2 + 1
= (89 + 86 + ......................+ 2) + (88 + 85+.........................+ 1)
= (30/2)(2 + 89) + (30/2)(1 + 88)
= 15 ( 180)
= 2700
2700 Triangles