Carcass wrote:
If the degree measures of the angles of a triangle are in the ratio 3 : 4 : 5, what is the degree measure of the smallest angle?
(A) 15°
(B) 30°
(C) 45°
(D) 60°
(E) 75°
Here the following side represent as 90°-45°-45° right angled triangle
=(3, 4, 5) (5, 12, 13) (7, 24, 25) (8, 15, 17) etc
So the smallest angle = 45°
Next method,
Let the x= smallest angle,
we can also re write as: 3x + 4x + 5x = 180
or 12x = 180
or x= 15
Therefore the smallest angle = 3x = 3*15 = 45°
A 45-45-90 triangle would have a ratio of x : x : \sqrt{2} ... your logic for first explanation is wrong but you came to a right conclusion by luck. Triangle can't be right-angled because then a 45 degree angle + 90 degrees means your third angle is also 45. 45:45:90 cannot have a 3:4:5 ratio because 3:4:5 is not x : x : \sqrt{2}
close
76% (00:27) correct
