Question

what is the angle between a 8N force and 6N force so that their resultan is 10N
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Answer 1

$\large \underline \bold{Given :-}$

$\: \: \: \: \: \:$$\small \bold{F1 = 8 \: N}$

$\: \: \: \: \: \:$$\small \bold{F2 = 6 \: N}$

$\small \bold{Resultant \: of \: F1 \: and \: F2 = F = 10 \: N}$

$\large \underline \bold{To \: Find :-}$

$\small \bold{What's \: the \: angle \: between \: 8 \: N \: and \: 6 \: N \: force \: ?}$

$\large \underline \bold{Usable \: Resultant \: Formula :-}$

$\small \bold{| \vec{F} | =\sqrt{F1^{2} + F2^{2} + 2F1 F2 CosO}}$

$\large \underline \bold{Solution :-}$

$\small \bold{On \: Using \: above \: resultant \: formula -}$

$\small \bold{F =\sqrt{F1^{2} + F2^{2} + 2F1 F2 CosO}}$

$\small \bold{10 =\sqrt{8^{2} + 6^{2} + 2(8)(6)CosO}}$

$\small \bold{100 = 64 + 36 + 96CosO}$

$\small \bold{\cancel{100} =\cancel{100} + 96CosO}$

$\: \: \: \: \:$$\small \bold{0 = 96CosO}$

$\: \: \: \: \:$$\small \bold{96CosO = 0}$

$\: \: \: \: \: \:$$\small \bold{CosO = 0}$

$\: \: \: \: \: \: \: \: \:$$\small \bold{O = 90}$°