A mass m=255kg hangs from a horizontal ceiling by two cables, one of length 3.0m and the other 4.0m; the two cables subtend an angle of 90 degrees at the mass. What is the tension in each cable?

Have you draw a sketch?

Then, you'll see that the points of suspension of the cables are 5 m apart.

You have a mass of 255 kg, so, its weight is 2550 (from F=ma, taking a as 10m/s)

Since the system is in equilibrium, there is no resultant along the horizontal nor the vertical, the forces are balanced.

Therefore, the sum of vertical components of the tension in your two cables have to equal the weight you are suspending.

Vertical Force by cable 4m long = 4sin\alpha
Vertical Force by cable 3m long = 4sin\beta

Then, find the tensions in each of the cables through Pythagoras' Theorem.

Do you understand? :)

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