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Sagot :
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
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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