Respuesta :

foreveryoung11

Recall: SOHCAHTOA

Sin M = Opp/Hyp

Reference angle = M

Opp = 3√/21

Hyp = 15

Sin M = (3-√21)/15

Sin M = √21/5

Cos M = Adj/Hyp

Reference angle = M

Adj = 6

Hyp = 15

Cos M = 6/15

Cos M = 2/5

Tan M = Opp/Adj

Reference angle = M

Opp = 3√21

Adj = 6

Tan M = (3√21)/6

Tan M = √21/2

:Therefore: Sin M = √21/5

Cos M = 2/5

Tan M = √21/2

semsee45

Answer:

[tex]\sf \sin M=\boxed{\dfrac{\sqrt{21}}{5}}[/tex]

Step-by-step explanation:

Trigonometric ratios

[tex]\sf \sin(\theta)=\dfrac{O}{H}\quad\cos(\theta)=\dfrac{A}{H}\quad\tan(\theta)=\dfrac{O}{A}[/tex]

where:

  • [tex]\theta[/tex] is the angle
  • O is the side opposite the angle
  • A is the side adjacent the angle
  • H is the hypotenuse

Given:

  • [tex]\theta[/tex] = M
  • O = 3√21
  • A = 6
  • H = 15

[tex]\sf \sin M=\dfrac{3\sqrt{21}}{15}\quad\cos M=\dfrac{6}{15}\quad\tan M=\dfrac{3\sqrt{21}}{6}[/tex]

[tex]\implies \sf \sin M=\dfrac{3\sqrt{21}}{15}=\dfrac{\sqrt{21}}{5}[/tex]

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