contestada

Triangle A B C is shown. Angle C A B is a right angle. Angle A B C is 30 degrees and angle B C A is 60 degrees. The length of A C is 9 and the length of hypotenuse C B is 18. Which trigonometric ratios are correct for triangle ABC? Select three options. sin(C) = StartFraction StartRoot 3 EndRoot Over 2 EndFraction cos(B) = StartFraction StartRoot 2 EndRoot Over 3 EndFraction tan(C) = StartRoot 3 EndRoot sin(B) = One-half tan(B) = StartFraction 2 StartRoot 3 EndRoot Over 3 EndFraction

Respuesta :

olayemiolakunle65

Answer:

i. sin(C) = [tex]\frac{\sqrt{3} }{2}[/tex]

ii. tan(C) = [tex]\sqrt{3}[/tex]

iii. sin(B) = [tex]\frac{1}{2}[/tex]

Step-by-step explanation:

Given a right angled triangle ABC, with a right angle at A.

<ABC = [tex]30^{0}[/tex]

<BCA = [tex]60^{0}[/tex]

AC = 9 = 1

CB = 18 = 2

Applying Pythagoras theorem to ΔABC, we have;

AB = [tex]\sqrt{BC^{2} - AC^{2} }[/tex]

    = [tex]\sqrt{2^{2} - 1^{2} }[/tex]

   = [tex]\sqrt{3}[/tex]

Thus applying the trigonometric ratios, it would be observed that;

i. sin(C) = [tex]\frac{\sqrt{3} }{2}[/tex]

ii. tan(C) = [tex]\sqrt{3}[/tex]

iii. sin(B) = [tex]\frac{1}{2}[/tex]

pristina

The correct trigonometric ratios are

[tex]sin\,C =\frac{\sqrt{3} }{2}[/tex]

[tex]tan\,C=\sqrt{3}[/tex]

[tex]Sin \,B=\frac{1}{2}[/tex]

Given that ABC is a right-angled triangle with the hypotenuse 18 cm and one of the sides 9 cm.

  • ie; [tex]CB = 18\,cm[/tex]
  • [tex]AC=9\,cm[/tex]

Therefore, using the Pythagoras theorem, we have;

[tex]AB^2 + AC^2 = BC^2\\\implies AB^2 = BC^2-AC^2[/tex]

  • So; [tex]AB^2 = \sqrt{18^2 - 9^2} = \sqrt{243} = 9\sqrt{3} \,cm[/tex]

From the figure attached below;

  • [tex]sin\,C = \frac{AB}{BC} =\frac{9\sqrt{3} }{18} =\frac{\sqrt{3} }{2}[/tex]
  • [tex]tan\,C=\frac{AB}{AC} =\frac{9\sqrt{3} }{9} =\sqrt{3}[/tex]
  • [tex]Sin \,B=\frac{AC}{BC} =\frac{9 }{18} =\frac{1}{2}[/tex]
  • [tex]cos\,B=\frac{AB}{BC}=\frac{9\sqrt{3} }{18}=\frac{\sqrt{3}}{2}[/tex]
  • [tex]tan\,B=\frac{AC}{AB}= \frac{9}{9\sqrt{3} } = \frac{1}{\sqrt{3}}[/tex]

Learn more about trigonometric ratios here:

https://brainly.com/question/12172664

Ver imagen pristina

Otras preguntas