Question

find the angle between two forces 4N and 6N so that their resultant is √69 N​

Answer 1

Angle = 69.26°

Given :-

$\sf{F1 = 4 \: N}$

$\sf{F2 = 6 \: N}$

$\sf{| F | =\sqrt{69} \: N}$

To Find :-

$\sf{angle \: between \: F1 \: and \: F2 = ? \: }$

Using Formula :-

Resultant of two Forces -

$\sf{\sf\boxed{| F | =\sqrt{F1^{2} + F2^{2} + 2F1 F2 CosO}}}$

Solution :-

By Using Resultant Formula -

$\sf{\sqrt{69} =\sqrt{(4)^{2} + (6)^{2} + 2(4)(6) CosO}}$

DOING SQUARE BOTH SIDE -

$\sf{69 = (4)^{2} + (6)^{2} + 2(4)(6) CosO}$

$\sf{69 = 16 + 36 + 48 CosO}$

$\sf{69 = 52 + 48 CosO}$

$\sf{48 CosO = 69 - 52}$

$\sf{48 CosO = 17}$

$\sf{CosO =\dfrac{17}{48}}$

$\sf{O = Cos^{-1}(\dfrac{17}{48})}$

$\sf{O = Cos^{-1}(0.3542)}$

O = 69.26°

The angle between 4 N and 6 N is 69.26° .