Question

me ajudem por favor só responda se souber !!!​

Answer 1

Resposta:

z² = 16 . 25

z² = 400

z = √400

z = 20

Answer 2

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$\Huge\green{\boxed{\rm~~~\gray{z}~\pink{=}~\blue{20}~~~}}$

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$\bf\large\green{\underline{\qquad \qquad \qquad \qquad \qquad \qquad \qquad \qquad}}$

$\green{\rm\underline{EXPLICAC_{\!\!\!,}\tilde{A}O\ PASSO{-}A{-}PASSO\ \ \ }}$✍

❄☃ $\sf(\gray{+}~\red{cores}~\blue{com}~\pink{o}~\orange{App}~\green{Brainly})$ ☘☀

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☺lá novamente, Lara. Vamos a mais um exercício❗ Acompanhe a resolução abaixo e após o resultado você encontrará um link com mais informações sobre Lei dos Senos que talvez te ajude com exercícios semelhantes no futuro. ✌

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$\sf (Esta~imagem~n\tilde{a}o~\acute{e}~visualiz\acute{a}vel~pelo~App~Brainly$ ☹ )

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$\setlength{\unitlength}{0.95cm}\begin{picture}(6,5)\thicklines\put(0,0){\line(1,0){9.7}}\put(0,0){\line(2,3){3}}\put(3,4.5){\line(3,-2){6.7}}\put(3,0){\line(0,1){4.5}}\bezier(0.45,0.65)(0.8,0.6)(0.9,0)\put(0.4,0.2){ \alpha }\bezier(8.7,0.65)(8.5,0.7)(8.45,0)\put(8.7,0.2){ \beta }\put(3.5,4.5){A}\put(-0.6,0){B}\put(9.9,0){C}\put(2.5,0.5){\line(1,0){1}}\put(2.5,0){\line(0,1){0.5}}\put(3.5,0){\line(0,1){0.5}}\put(3.7,0.2){D}\put(2.77,0.23){\circle*{0.1}}\put(3.27,0.23){\circle*{0.1}}\put(3.2,2){z}\end{picture}$

$\sf (Esta~imagem~n\tilde{a}o~\acute{e}~visualiz\acute{a}vel~pelo~App~Brainly$ ☹ )

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☔ Temos que ABC, ABD e ACD são triângulos semelhantes tendo em vista que sendo α e β complementares então os três triângulos são compostos pelos ângulos α, β e 90º. Com essa informação podemos utilizar a Lei dos Senos para analisar em ABD

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➡ $\large\sf\blue{ \dfrac{z}{sen(\alpha)} = \dfrac{16}{sen(\beta)}}$

➡ $\large\sf\blue{ \dfrac{sen(\alpha)}{sen(\beta)} = \dfrac{z}{16}}$

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☔ Em ADC

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➡ $\large\sf\blue{ \dfrac{z}{sen(\beta)} = \dfrac{25}{sen(\alpha)}}$

➡ $\large\sf\blue{ \dfrac{sen(\alpha)}{sen(\beta)} = \dfrac{25}{z}}$

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☔ Sendo $\sf \dfrac{sen(\alpha)}{sen(\beta)} = \dfrac{sen(\alpha)}{sen(\beta)}$ então temos que

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➡ $\large\sf\blue{ \dfrac{z}{16} = \dfrac{25}{z}}$

➡ $\large\sf\blue{z^2 = 400}$

➡ $\large\sf\blue{\sqrt{z^2} = \pm \sqrt{400}}$

➡ $\large\sf\blue{z = \pm 20}$

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☔ Como z será sempre um valor positivo então assumiremos somente sua solução positiva

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➡ $\large\sf\blue{ z = 20 }$

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$\Huge\green{\boxed{\rm~~~\gray{z}~\pink{=}~\blue{20}~~~}}$ ✅

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$\bf\large\red{\underline{\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad}}$

✈ Lei dos Senos (https://brainly.com.br/tarefa/35868408)

$\bf\large\red{\underline{\qquad\qquad\qquad\qquad\qquad\qquad\qquad\quad}}$✍

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$\bf\large\red{\underline{\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad}}$☁

☕ $\bf\Large\blue{Bons\ estudos.}$

($\large\orange{D\acute{u}vidas\ nos\ coment\acute{a}rios}$) ☄

$\bf\large\red{\underline{\qquad \qquad \qquad \qquad \qquad \qquad \quad }}\LaTeX$✍

❄☃ $\sf(\gray{+}~\red{cores}~\blue{com}~\pink{o}~\orange{App}~\green{Brainly})$ ☘☀

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$\gray{"Absque~sudore~et~labore~nullum~opus~perfectum~est."}$