Question

Determine a medida x em cada triângulo.

Answer 1

Resposta:

Explicação passo-a-passo:

1)

cos 45=cat adj/hipotenusa

√2/2=3√2/x

√2x=2.3√2

x=6√2/√2

x=6

2)tg 30=cat oposto/cat adj

tg30=x/2√3

√3/3=x/2√3

3x=2√3√3

3x=2.3

x=2

3

sen 60=cat oposto/hipotenusa

√3/2=x/6√3

2x=6√3√3

2x=6.3

2x=18

x=9

Answer 2

Explicação passo-a-passo:

a)

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

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

$\sf x\sqrt{2}=2\cdot3\sqrt{2}$

$\sf x\sqrt{2}=6\sqrt{2}$

$\sf x=\dfrac{6\sqrt{2}}{\sqrt{2}}$

$\sf x=6$

b)

$\sf tg~30^{\circ}=\dfrac{cateto~oposto}{cateto~adjacente}$

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

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

$\sf 3x=2\cdot3$

$\sf 3x=6$

$\sf x=\dfrac{6}{3}$

$\sf x=2$

c)

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

$\sf \dfrac{\sqrt{3}}{2}=\dfrac{x}{6\sqrt{3}}$

$\sf 2x=6\sqrt{3}\cdot\sqrt{3}$

$\sf 2x=6\cdot3$

$\sf 2x=18$

$\sf x=\dfrac{18}{2}$

$\sf x=9$