Solve for the resultant (kN) of the concurrent forces shown.        Given:        P =20 kN; Q = 15 kN; R = 5 kN; S = 5 kN        θ = 60°; α = 45°; β = 19°.QUESTION 1ANSWERA.25.55B.24.33C.39.16D.40.12

The problem involves calculating the resultant of concurrent forces. Here are the steps to solve it:

1. First, we need to resolve each force into its horizontal and vertical components.

2. For force P (20 kN), it's already acting horizontally so its horizontal component is 20 kN and vertical component is 0.

3. For force Q (15 kN), it's acting at an angle of 60 degrees. So, its horizontal component is Qcos(60) = 15cos(60) = 7.5 kN and vertical component is Qsin(60) = 15sin(60) = 12.99 kN.

4. For force R (5 kN), it's acting at an angle of 45 degrees. So, its horizontal component is Rcos(45) = 5cos(45) = 3.54 kN and vertical component is Rsin(45) = 5sin(45) = 3.54 kN.

5. For force S (5 kN), it's acting at an angle of 19 degrees. So, its horizontal component is Scos(19) = 5cos(19) = 4.67 kN and vertical component is Ssin(19) = 5sin(19) = 1.59 kN.

6. Now, add up all the horizontal components to get the total horizontal component (H) and all the vertical components to get the total vertical component (V). H = 20 + 7.5 + 3.54 + 4.67 = 35.71 kN and V = 0 + 12.99 + 3.54 + 1.59 = 18.12 kN.

7. The resultant force (R) can be found using the Pythagorean theorem: R = sqrt(H^2 + V^2) = sqrt((35.71)^2 + (18.12)^2) = 39.16 kN.

So, the answer is C. 39.16 kN.