Question

Calcule os valores das incógnitas dos triângulos retângulos abaixo: a) 32√3/3, b) y= ½, c) 9√3, d) 20√2

Answer 1

Resposta:

Leia abaixo

Explicação passo-a-passo:

a.

cos 30° = 16/x

√3/2 = 16/x

x = 32/√3

x = 32√3/3

b.

sen y = 13/26

sen y = 1/2

y = 30°

c.

sen 60° = w/18

√3/2 = w/18

w = 9√3

d.

cos 45° = 20/z

√2/2 = 20/z

z = 20√2

Answer 2

Explicação passo-a-passo:

a)

$\sf cos~30^{\circ}=\dfrac{cateto~adjacente}{hipotenusa}$

$\sf \dfrac{\sqrt{3}}{2}=\dfrac{16}{x}$

$\sf x\sqrt{3}=2\cdot16$

$\sf x\sqrt{3}=32$

$\sf x=\dfrac{32}{\sqrt{3}}$

$\sf x=\dfrac{32}{\sqrt{3}}\cdot\dfrac{\sqrt{3}}{\sqrt{3}}$

$\sf \red{x=\dfrac{32\sqrt{3}}{3}}$

b)

$\sf sen~y=\dfrac{cateto~oposto}{hipotenusa}$

$\sf sen~y=\dfrac{13}{26}$

$\sf sen~y=\dfrac{13\div13}{26\div13}$

$\sf sen~y=\dfrac{1}{2}$

Lembre-se $\sf sen~30^{\circ}=\dfrac{1}{2}$

Logo, $\sf \red{y=30^{\circ}}$

c)

$\sf sen~60^{\circ}=\dfrac{cateto~oposto}{hipotenusa}$

$\sf \dfrac{\sqrt{3}}{2}=\dfrac{w}{18}$

$\sf 2\cdot w=18\sqrt{3}$

$\sf w=\dfrac{18\sqrt{3}}{2}$

$\sf \red{w=9\sqrt{3}}$

d)

$\sf cos~45^{\circ}=\dfrac{cateto~adjacente}{hipotenusa}$

$\sf \dfrac{\sqrt{2}}{2}=\dfrac{20}{z}$

$\sf z\sqrt{2}=2\cdot20$

$\sf z\sqrt{2}=40$

$\sf z=\dfrac{40}{\sqrt{2}}$

$\sf z=\dfrac{40}{\sqrt{2}}\cdot\dfrac{\sqrt{2}}{\sqrt{2}}$

$\sf z=\dfrac{40\sqrt{2}}{2}$

$\sf \red{z=20\sqrt{2}}$