Question

Determine as medidas desconhecidas indicadas nas
figuras a seguir.
​

Answer 1

Caso tenha problemas para visualizar a resposta experimente abrir pelo navegador

https://brainly.com.br/tarefa/35650545

$\sf 5^2=z^2+6^2-2\cdot z\cdot6\cdot cos(55^\circ)\\\sf 25=z^2+36-12z\cdot0,57\\\sf z^2+36-6,84z=25\\\sf z^2-6,84z+36-25=0\\\sf z^2-6,84z+11=0\\\sf\Delta=46,78-44=2,78$

$\sf z=\dfrac{6,84\pm2,78}{2}\\\sf z_1=4,81\\\sf z_2=2,03$

Vamos descobrir o valor de x pela lei dos senos:

Se z=4,81

$\sf\dfrac{5}{sen(55^\circ)}=\dfrac{z}{sen(x)}\\\sf 5sen(x)=zsen(55^\circ)\\\sf 5sen(x)=4,81\cdot 0,81\\\sf sen(x)=\dfrac{3,89}{5}\\\sf sen(x)=0,77\\\sf x=arcsen(77)\\\sf x=50,35^\circ\\\sf y=180^\circ-50,35^\circ-55^\circ\\\sf y=74,65^\circ$

Se z=2,03

$\sf\dfrac{5}{sen(55^\circ)}=\dfrac{z}{sen(x)}\\\sf5sen(x)=2,03sen(55^\circ)\\\sf 5sen(x)=1,66\\\sf sen(x)=\dfrac{1,66}{5}\\\sf sen(x)=0,33\\\sf x=arcsen(0,33)\\\sf x=19,26^\circ\\\sf y=180^\circ-19,26^\circ-55^\circ\\\sf y=105,74^\circ$