Question

pls solve this question​

Answer 1

Answer:

The answer is 13

sin@ = 12/13

then

cos @ = 5/13

substitute the values

then answer will be 13

I hope this will be correct

Answer 2

Solution :

$\bigstar$We have sin Ф = 12/13

$\longrightarrow\sf{sin\theta=\dfrac{12}{13} =\bigg[\dfrac{Perpendicular}{Hypotenuse} \bigg]}$

Diagram :

$\setlength{\unitlength}{1.5cm}\begin{picture}(6,2)\linethickness{0.4mm}\put(7.7,2.9){\large\sf{A}}\put(7.7,1){\large\sf{B}}\put(10.6,1){\large\sf{C}}\put(8,1){\line(1,0){2.5}}\put(8,1){\line(0,2){1.9}}\qbezier(10.5,1)(10,1.4)(8,2.9)\put(7.2,2){\large\sf{12\:unit}}\put(8.8,0.7){\large\sf{b}}\put(9.4,1.9){\large\sf{13\:unit}}\put(8.2,1){\line(0,1){0.2}}\put(8,1.2){\line(3,0){0.2}}\end{picture}$

$\underline{\boldsymbol{By\:using\:Pythagoras\:theorem\::}}}}$

$\longrightarrow\sf{(Hypotenuse)^{2} =(Base)^{2} +(Perpendicular)^{2} }\\\\\longrightarrow\sf{(AC)^{2} =(BC)^{2} +(AB)^{2} }\\\\\longrightarrow\sf{(13)^{2} =(BC)^{2}+(12)^{2} }\\\\\longrightarrow\sf{169=(BC)^{2} +144}\\\\\longrightarrow\sf{(BC)^{2} =169-144}\\\\\longrightarrow\sf{(BC)^{2} =25}\\\\\longrightarrow\sf{BC=\sqrt{25} }\\\\\longrightarrow\bf{BC=5\:unit}$

Now;

$\boxed{\bf{Evaluate\::}}}$

$\mapsto\sf{\bigg(\dfrac{2sin\theta-3cos\theta}{4sin\theta-9cos\theta} \bigg)}\\\\\\\mapsto\sf{\Bigg(\dfrac{2\dfrac{Perpendicular}{Hypotenuse} -3\dfrac{Base}{Hypotenuse} }{4\dfrac{Perpendicular}{Hypotenuse}-9\dfrac{Base}{Hypotenuse} } \Bigg)}\\\\\\\mapsto\sf{\Bigg(\dfrac{2\dfrac{AB}{AC} -3\dfrac{BC}{AC} }{4\dfrac{AB}{AC}-9\dfrac{BC}{AC} }\Bigg)}\\\\\\\mapsto\sf{\Bigg(\dfrac{2\times \dfrac{12}{13} -3\times \dfrac{5}{13} }{4\times \dfrac{12}{13}-9\times \dfrac{5}{13} }\Bigg)}$

$\mapsto\sf{\Bigg(\dfrac{ \dfrac{24}{13} - \dfrac{15}{13} }{ \dfrac{48}{13}-\dfrac{45}{13} }\Bigg)}\\\\\\\mapsto\sf{\Bigg(\dfrac{ \dfrac{24-15}{13} }{ \dfrac{48-45}{13} }\Bigg)}\\\\\\\mapsto\sf{\dfrac{ \dfrac{9}{13} }{ \dfrac{3}{13} }}\\\\\\\mapsto\sf{\dfrac{9}{\cancel{13}} \times \dfrac{\cancel{13}}{3} }\\\\\\\mapsto\sf{\cancel{\dfrac{9}{3}} }\\\\\mapsto\bf{3}$

Thus;

The value will be 3 .