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Find the resultant of two forces 6N and 5N which are inclined to each other at 3...

Question

Find the resultant of two forces 6N and 5N which are inclined to each other at 30".

Options

A) 12.2N

B) 8.7N

C) 10.6N

D) 9.5N

E) 3N

The correct answer is E.

Explanation:

By cosine rule
$$R^2 = 5^2 + 6^2 - 2(5)(6)\cos 30^{\circ}$$
$$R^2 = 25 + 36 - 60(0.866)$$
$$= 25 + 36 - 51.96$$
$$61 - 52 = 9$$
$$R = \sqrt{9} = 3$$N

Dicussion (1)

• By cosine rule
$$R^2 = 5^2 + 6^2 - 2(5)(6)\cos 30^{\circ}$$
$$R^2 = 25 + 36 - 60(0.866)$$
$$= 25 + 36 - 51.96$$
$$61 - 52 = 9$$
$$R = \sqrt{9} = 3$$N