two forces with magnitudes of 90 and 50 pounds act on an object at angles of 30 and 160, respectively. find the direction and magnitude of the resultant force.

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Magnitude of he two forces are $\"\"$ lb and $\"\"$ lb.

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Two forces acting on an object at an angles of $\"\"$ and $\"\"$ .

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Find the horizontal and vertical components of $\"\"$ .

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Horizontal component of vector $\"\"$ is $\"\"$

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Vertcal components of vector $\"\"$ is $\"\"$ .

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Therefore, $\"\"$ and $\"\"$ .

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$\"\"$ and $\"\"$

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Write the force $\"\"$ in vector form.

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$\"\"$

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Substitute corresponding values.

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$\"\"$ .

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Write the force $\"\"$ in vector form.

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$\"\"$

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Substitute corresponding values.

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$\"\"$ .

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Resultant force vector $\"\"$ .

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$\"\"$

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$\"\"$ .

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Find the magnitude and direction of the resultant force $\"\"$ .

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Magnitude of vector $\"\"$ is $\"\"$ .

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Direction angle of the vector $\"\"$ is $\"\"$ .

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Thus, $\"\"$

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$\"\"$ .

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$\"\"$

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Direction angle of the resultant vector is $\"\"$

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$\"\"$ .

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$\"\"$

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