Question

Determine as medidas dos catetos no triângulo retângulo a seguir:

Answer 1

Explicação passo-a-passo:

1)

• $\sf sen~30^{\circ}=\dfrac{cateto~oposto}{hipotenusa}$

$\sf \dfrac{1}{2}=\dfrac{x}{100}$

$\sf 2x=100\cdot1$

$\sf 2x=100$

$\sf x=\dfrac{100}{2}$

$\sf \red{x=50~cm}$

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

$\sf \dfrac{\sqrt{3}}{2}=\dfrac{y}{100}$

$\sf 2y=100\sqrt{3}$

$\sf y=\dfrac{100\sqrt{3}}{2}$

$\sf \red{y=50\sqrt{3}~cm}$

2)

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

$\sf \dfrac{\sqrt{3}}{3}=\dfrac{x}{25}$

$\sf 3x=25\sqrt{3}$

$\sf \red{x=\dfrac{25\sqrt{3}}{3}~cm}$

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

$\sf \dfrac{\sqrt{3}}{2}=\dfrac{25}{y}$

$\sf y\sqrt{3}=25\cdot2$

$\sf y\sqrt{3}=50$

$\sf y=\dfrac{50}{\sqrt{3}}$

$\sf y=\dfrac{50}{\sqrt{3}}\cdot\dfrac{\sqrt{3}}{\sqrt{3}}$

$\sf \red{y=\dfrac{50\sqrt{3}}{3}~cm}$

3)

$\sf sen~30^{\circ}=\dfrac{cateto~oposto}{hipotenusa}$

$\sf \dfrac{1}{2}=\dfrac{x}{8}$

$\sf 2x=8\cdot1$

$\sf 2x=8$

$\sf x=\dfrac{8}{2}$

$\sf \red{x=4}$

4)

$\sf tg~42^{\circ}=\dfrac{cateto~oposto}{cateto~adjacente}$

$\sf 0,9=\dfrac{64}{d}$

$\sf 0,9d=64$

$\sf d=\dfrac{64}{0,9}$

$\sf d=\dfrac{640}{9}$

$\sf \red{d=71,11~m}$

5)

$\sf sen~30^{\circ}=\dfrac{cateto~oposto}{hipotenusa}$

$\sf \dfrac{1}{2}=\dfrac{h}{5000}$

$\sf 2h=5000\cdot1$

$\sf 2h=5000$

$\sf h=\dfrac{5000}{2}$

$\sf \red{h=2500~m}$

6)

$\sf sen~39^{\circ}=\dfrac{cateto~oposto}{hipotenusa}$

$\sf 0,63=\dfrac{h}{18}$

$\sf h=0,63\cdot18$

$\sf \red{h=11,34~m}$

7)

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

$\sf \dfrac{\sqrt{3}}{3}=\dfrac{h}{60}$

$\sf 3h=60\sqrt{3}$

$\sf h=\dfrac{60\sqrt{3}}{3}$

$\sf \red{h=20\sqrt{3}~m}$