Question

alguien me ayuda con mi tarea ?

Answer 1

           $\underline{\LARGE\textbf{RAZONES TRIGONOM\'ETRICAS}}$

$\red{\texttt{RAZONES TRIGONOM\'ETRICAS}}$

$\text{En este problema solo utilizaremos estas:}\\\\\LARGE\boxed{\mathbf{Cos(x)=\frac{Cateto~adyacente}{Hipotenusa}}}\\\\\boxed{\mathbf{Tg(x)=\frac{Cateto~opuesto}{Cateto~adyacente}}}$

$\red{\texttt{TEOREMA DE PIT\'AGORAS}}$

$\LARGE\boxed{\mathbf{cateto^2+cateto^2=hipotenusa^2}}$

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Hallamos el cateto que falta.

$\mathrm{cateto^2+3^2=(3\sqrt{2})^2 }\\\\\mathrm{cateto^2+9=18 }\\\\\mathrm{cateto^2=9 }\\\\\boxed{\mathrm{cateto=3 }}$

Y hallamos P

$\mathrm{P=\sqrt{2}\cos\alpha+ 5\tan\alpha }\\\\\mathrm{P=\sqrt{2}(\dfrac{3}{3\sqrt{2} })+5(\dfrac{3}{3}) }\\\\\mathrm{Simplificamos}\\\\\mathrm{P={\sqrt{2}}(\dfrac{3}{3{\sqrt{2} }})+5(\dfrac{3}{3}) }\\\\\mathrm{P=\frac{3}{3}+5(1) }\\\\\mathrm{P=1+5(1) }\\\\\mathrm{P=1+5 }\\\\\Large\boxed{\mathbf{P=6 }}$

RPTA: P = 6