Use the parallelogram rule to find the magnitude of the resultant force for the two forces shown in each figure. Round answers to the nearest tenth.
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For each pair of vectors u and v with angle θ between them, sketch the resultant.

|u| = 12, |v| = 20, θ = 27°

For each pair of vectors u and v with angle θ between them, sketch the resultant.

|u| = 20, |v| = 30, θ = 30°

Use the parallelogram rule to find the magnitude of the resultant force for the two forces shown in each figure. Round answers to the nearest tenth.

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Write each vector in the form 〈a, b〉. Write answers using exact values or to four decimal places, as appropriate.

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Two forces act on a point in the plane. The angle between the two forces is given. Find the magnitude of the resultant force.

forces of 250 and 450 newtons, forming an angle of 85°

Two forces act on a point in the plane. The angle between the two forces is given. Find the magnitude of the resultant force.

forces of 116 and 139 lb, forming an angle of 140° 50′

Two tugboats are pulling a disabled speedboat into port with forces of 1240 lb and 1480 lb. The angle between these forces is 28.2°. Find the direction and magnitude of the equilibrant.

Two rescue vessels are pulling a broken-down motorboat toward a boathouse with forces of 840 lb and 960 lb. The angle between these forces is 24.5°. Find the direction and magnitude of the equilibrant.