The pulley system shown in figure, MQ=10 in., NP=3 in., and QP=24 in. Find MN

We can get QN by Pythagorean theorem:

QN = √24² + 3² = 24.19

We can get angle NQP by:

tan NQP = 3/24

NQP = 7.13°

With this, we can get angle MQN

MQN = 90 - 7.13

MQN = 82.87°

By cosine law, we can get MN

MN = √[10² + 24.19² - 2 (10) (24.19) cos82.87]

MN = 25 in