# Question #ce495

Apr 28, 2016

69.3N

#### Explanation:

The diagram below will help

The system is in equilibrium so the vertical and horizontal force must balance.

Considering vertical forces:

$T 1 \cdot \cos 50 + T 2 \cdot \cos 45 = m g$

$m g = 10 \cdot 9.81 = 98.1 N$

And Horizontal force

$T 1 \cdot \sin 50 = T 2 \cdot \sin 45$

Rearranging
$T 2 = T 1 \cdot \sin \frac{50}{\sin} 45$
And substituting this into the first equation

$T 1 \cdot \cos 50 + T 1 \ast \sin \frac{50}{\sin} 45 \cdot \cos 45 = 98.1$

$T 1 \left(\cos 50 + \sin \frac{50}{\sin} 45 \cdot \cos 45\right) = 98.1$

Solving gives $T 1 = 69.63 N$