Final answer:
To determine the horizontal and vertical components of reactions at pin A and rocker B, use trigonometric functions to decompose each vector into its x and y components based on their magnitudes and angles with the x-axis. Horizontal components are found using cosine, and vertical components are calculated with sine.
Step-by-step explanation:
To determine the horizontal and vertical components of the reactions at the pin A and rocker B, one must first set up a coordinate system.
Each vector's components along the x-axis (horizontal) and y-axis (vertical) can be found using trigonometric relationships.
The horizontal component of a vector is found by multiplying the magnitude of the vector by the cosine of the angle it makes with the x-axis, represented by the equation Ax = A × cos(θ).
Similarly, the vertical component is found by multiplying the magnitude of the vector by the sine of the angle, represented by the equation Ay = A × sin(θ).
For vector A with a magnitude of 53.0 m and an angle of 20.0° with the x-axis, its horizontal component Ax will be A × cos(20.0°).
Similarly, the horizontal component of vector B with a magnitude of 34.0 m and an angle of 63.0° will be Bx = B × cos(63.0°).
The vertical components can be computed in a similar manner using sine.
After finding the components of each vector, you can determine the reaction components at the points A and B using equilibrium equations.