Chapter 1: Resolution of Forces

Explain how Pythagoras' theorem and trigonometry can be used to calculate the magnitude and direction of forces acting on a structure.

• By using the sine and cosine functions to resolve forces into components and applying Pythagoras' theorem to find the resultant force.

• By using only the tangent function to find the angle of the force.

• By applying Pythagoras' theorem directly to find the angle of the force.

• By using trigonometry to calculate the mass of the structure.

What is the vertical component (Fv) of a 90N force acting at a 30° angle?

• Fv = 45N

• Fv = 60N

• Fv = 75N

• Fv = 90N

What is the horizontal component (Fh) of a 90N force acting at a 30° angle?

• Fh = 77.94N

• Fh = 45N

• Fh = 90N

• Fh = 60N

Resolve the following force into its horizontal and vertical components: 10N at 30°.

• Horizontal: 5N, Vertical: 8.66N

• Horizontal: 8.66N, Vertical: 5N

• Horizontal: 10N, Vertical: 0N

• Horizontal: 0N, Vertical: 10N

Resolve the following force into its horizontal and vertical components: 6kN at 60°.

• Horizontal: 3 kN, Vertical: 5.2 kN

• Horizontal: 5.2 kN, Vertical: 3 kN

• Horizontal: 4 kN, Vertical: 4 kN

• Horizontal: 3 kN, Vertical: 3 kN

Resolve the following force into its horizontal and vertical components: 200N at 40°.

• Horizontal: 153.2N, Vertical: 128.6N

• Horizontal: 128.6N, Vertical: 153.2N

• Horizontal: 200N, Vertical: 0N

• Horizontal: 0N, Vertical: 200N

Resolve the following force into its horizontal and vertical components: 25kN at 70°.

• Horizontal: 8.55 kN, Vertical: 23.49 kN

• Horizontal: 23.49 kN, Vertical: 8.55 kN

• Horizontal: 21.37 kN, Vertical: 9.13 kN

• Horizontal: 9.13 kN, Vertical: 21.37 kN

Find the resultant force given the following forces: 10kN at 30°, 80kN at 60°, and 30kN vertically upwards. Use the diagram to assist in your calculation.

• 100kN at 45°

• 110kN at 60°

• 120kN at 75°

• 130kN at 90°

What is the value of R_V?

• 44.28

• 31.34

• 54.00

• 55.00

Step 4: Use trigonometry to calculate the missing angle (Θ). What is the value of Θ?

• 30°

• 45°

• 55°

• 60°