Respuesta :

Ashraf82

Answer:

Figure 4 ⇒ x = [tex]\frac{10\sqrt{3}}{3}[/tex] = 5.774

                   y = [tex]\frac{5\sqrt{3}}{3}[/tex] = 2.887

Figure 5 ⇒ x = 7

                   y = [tex]\frac{7\sqrt{3} }{3}[/tex] = 4.041

Step-by-step explanation:

Figure 4:

∵ The Δ is right triangle

∴ Use trigonometry function

∵ 5/x = sin(60°)

∴ x = 5/sin(60°) = [tex]\frac{10\sqrt{3} }{3}[/tex] = 5.774

∵ 5/y = tan(60°)

∴ y = 5/tan(60°) = [tex]\frac{5\sqrt{3}}{3}[/tex] = 2.887

Figure 5:

∵ The Δ is right triangle

∴ Use trigonometry function

∵ [tex]\frac{x}{\frac{14\sqrt{3}}{3}}[/tex] = sin(60°)

∴ x = [tex]\frac{14\sqrt{3}}{3}[/tex]×sin(60°) = 7

∵ [tex]\frac{y}{\frac{14\sqrt{3}}{3}}[/tex] = cox(60°)

∴ y = [tex]\frac{14\sqrt{3}}{3}[/tex]×cos(60°)=[tex]\frac{7\sqrt{3}}{3}[/tex] = 4.041

tramserran

A 30°- 60°- 90° triangle has corresponding sides of:  b - b√3 - 2b

The sides are OPPOSITE of the angle (the side the angle is not touching)

4. Answer:  [tex]\bold{x = 7,\quad y=\dfrac{7\sqrt3}{3}}[/tex]

Step-by-step explanation:

[tex]90^o: 2b = \dfrac{14\sqrt3}{3}\\\\\\30^o: b=y\\\\.\quad \dfrac{1}{2}\cdot \dfrac{14\sqrt3}{3}=y\\\\.\quad \dfrac{7\sqrt3}{3}=y\\\\\\60^o: b\sqrt3=x\\\\.\quad \bigg(\dfrac{7\sqrt3}{3}\bigg)\sqrt3=x\\\\.\quad \dfrac{7\cdot 3}{3}=x\\\\.\quad 7=x\\[/tex]

5. Answer:  [tex]\bold{x=\dfrac{10\sqrt3}{3},\quad y=\dfrac{5\sqrt3}{3}}[/tex]

Step-by-step explanation:

[tex]60^o: b\sqrt3=5\\\\30^o:b=y\\\\.\qquad \dfrac{5}{\sqrt3}=y\\\\\\.\qquad \dfrac{5}{\sqrt3}\bigg(\dfrac{\sqrt3}{\sqrt3}\bigg)=y\\\\\\.\qquad \dfrac{5\sqrt3}{3}=y\\\\\\90^o: 2b=x\\\\\\.\qquad 2\bigg(\dfrac{5\sqrt3}{3}\bigg)=x\\\\\\.\qquad \dfrac{10\sqrt3}{3}=x[/tex]

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