Question

A traffic sign is hanging from two wires. If the weight of the sign is 35 N, what are the tensions in the two wires as shown below?
Traffic sign hanging by two wires, making an angle of 56 and 45

Answer 1

the sign isn't moving , so the horizontal components are equal and opposite

the vertical components sum to 35 N

"making an angle of 56 and 45" ... with what?
... a little more description would help

Answer 2

Draw a position diagram showing the 2 wires and the suspended sign.
A very standard question if I assume the wires make angles of 45° and 56° along a horizontal.

draw a vector diagram of a triangle ABC, where AB is a vertical line representing the 35 N. AC the tension in the wire making a 45° angle, and CB the tension of the wire making the 56° angle. Simple geometry using parallel lines will given you
angle A = 45° , angle B = 34° and angle C = 101°
by the sine law:
BC/sin45 = 35/sin101 ----> BC = 35sin45/sin101 = appr 25.2 N
AC/sin34 = 34/sin101 ----> AC = 34sin45/sin101 = appr 24.5 N

Answer 3

T1*sin(180-56) + T2*sin45 = 35 N,
Eq1: 0.83T1 + 0.71T2 = 35.

T1*Cos(180-56) + T2*Cos45 = 0,
Eq2: -0.56T1 + 0.71T2 = 0,

Subtract Eq2 from Eq1:
Diff.: 1.39T1 = 35,
T1 = 25.2 N.

In Eq1, replace T1 with 25.2 and solve for T2.