a 10-kg mass is supported by two strings of length 5m and 7m attached to two pints in the celing 10m apart. find the tenion in each string

Answer 1

The net upward force exerted by the two strings must equal M g = 98 N

The strings make angles of A1 and A2 with the horizontal.
5 sin A1 = 7 sin A2.
5 cos A1 + 7 cos A2 = 10

Now you have to do some geometry.

25 sin^2 A1= 49 sin^2 A2
25 cos^2 A1 = 100 - 140 cosA2 + 49 cos^2 A2
25 = 100 -140cosA2 + 49
140 cosA2 = 124
A2 = 27.7 degrees
A1 = 40.5 degrees

Now write vertical and horizontal force balance equations and solve for the two rope tensions, T1 and T2.

T1 sinA1 + T2 sinA2 = 98 N
T1 cosA1 = T2 cosA2

Take it from there