In a ∆ABC, if 2 LA= 3 LB = 6 LC, then find A,B,C
see the prior post
http://www.jiskha.com/display.cgi?id=1470476726
if that's you too, stop changing names and wasting time with the same problem.
To find the values of angles A, B, and C in triangle ABC, we can use the fact that the sum of the angles in a triangle is always 180 degrees.
Let's assign the measure of angle A as "x." Since 2 times the measure of angle A is equal to the measure of angle B, we can write this relationship as:
2x = 3y ...(1)
Similarly, since 2 times the measure of angle A is equal to 6 times the measure of angle C, we can write this relationship as:
2x = 6z ...(2)
Now, we can solve these equations simultaneously to find the values of x, y, and z.
From equation (1), we can express y in terms of x:
y = (2/3)x
Substituting this value of y into equation (2), we can express z in terms of x:
2x = 6z
2x = 6(2/3)x
2x = 4x
2x - 4x = 0
-2x = 0
x = 0
Now that we have the value of x, we can find the measure of angles A, B, and C in terms of x:
A = x = 0 degrees
B = 2x = 2(0) = 0 degrees
C = 6z = 6(0) = 0 degrees
Therefore, in this case, all three angles of triangle ABC are equal to 0 degrees, which means the triangle is degenerate or completely flat.