How can I solve this?

The two forces form a parallelogram and the resultant force is a diagonal.
Hence, AD//BC and AB//DC

∠DAC = 74°29' - 43°9' = 31°20'
∠ACB = ∠DAC = 31°20'  (alt. ∠s, AD//BC)
∠ABC = 180° - ∠DAB = 180° - 74°29' = 105°31'  (int. ∠s, AD//BC)

In ΔABC:
AB / sin∠ACB = BC / sin∠CAB  (sine law)
151 / sin31°21' = BC / sin43°9'
BC = 151 × sin43°9' / sin 31°21'
BC = 198
Magnitude of the second force = 198 lb

AB / sin∠ACB = AC / sin∠ABC  (sine law)
151 / sin31°21' = AC/ sin105°31'
AC = 151 × sin105°31' / sin 31°21'
AC = 280
Magnitude of the resultant force = 280 lb

∠CAD = 74°29' - 43°09' = 31°20'

(151 lb)sin(-43°) + ADsin(31°20') = 0

Solve for AD, that is, the magnitude of force AD.

AC = ADcos(31°20') + (151 lb)cos(-43°)

<151 * cos(74d 29m) , 151 * sin(74d 29m)>
<F * cos(0) , F * sin(0)> =>> <F , 0>
<T * cos(43d 9m) , T * sin(43d 9m)>

T * sin(43d 9m) / (T * cos(43d 9m)) = (151 * sin(74d 29m) + 0) / (151 * cos(74d 29m) + F)

tan(43d 9m) = 151 * sin(74d 29m) / (F + 151 * cos(74d 29m))
(F + 151 * cos(74d 29m)) * tan(43d 9m) = 151 * sin(74d 29m)
F * tan(43d 9m) + 151 * cos(74d 29m) * tan(43d 9m) = 151 * sin(74d 29m)
F * tan(43d 9m) = (151 * sin(74d 29m) - 151 * cos(74d 29m) * tan(43d 9m))
F * tan(43d 9m) = 151 * (sin(74d 29m) - cos(74d 29m) * tan(43d 9m))
F * sin(43d 9m)/cos(43d 9m) = 151 * (1/cos(43d 9m)) * (sin(74d 29m) * cos(43d 9m) - cos(74d 29m) * sin(43d 9m))
F * sin(43d 9m) = 151 * (sin(74d 29m) * cos(43d 9m) - cos(74d 29m) * sin(43d 9m))
F * sin(43d 9m) = 151 * sin(74d 29m - 43d 9m)
F * sin(43d 9m) = 151 * sin(31d 20m)
F = 151 * sin(31d 20m) / sin(43d 9m)

So there's the 1st force.

151 * sin(74d 29m) + 0 = T * sin(43d 9m)
151 * sin(74d 29m) / sin(43d 9m) = T

151 * sin(31d 20m) / sin(43d 9m) =>
151 * sin((31 * 60 + 20) / 60 degrees) / sin((43 * 60 + 9) / 60 degrees) =>
151 * sin(1880/60) / sin(2589/60) =>
151 * sin(94/3) / sin(863/20) =>
151 * sin(94/3) / sin(43.15)

F = 151 * sin(94/3) / sin(43.15)
F = 114.8138715949481437397349649825....


151 * sin(74d 29m) / sin(43d 9m) =>
151 * sin((74 * 60 + 29) / 60) / sin(43.15) =>
151 * sin(4469/60) / sin(43.15) =>
212.741888702184375110965743358...

T = 212.741888...

To the nearest pounds

115 and 213