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PLEASE HELP!!! 70 POINTS

Use the image of triangle ABC to identify the ratios.

sin C= Blank
tan C= Blank
cos C= Blank

Options:

1. 8/7
2. 8/15
3. 15/17
4. 15/8
5. 17/8​

PLEASE HELP 70 POINTS Use the image of triangle ABC to identify the ratiossin C Blanktan C Blankcos C BlankOptions1 872 8153 15174 1585 178 class=


Answer :

Answer:

Step-by-step explanation:

To find the ratios of sine, cosine, and tangent for angle C in triangle ABC, we can use the side lengths of the triangle.

Given:

Side AB = 8

Side BC = 15

Side AC (the hypotenuse) = 17

Now, let's calculate the ratios:

Sine (sin) of angle C = Opposite / Hypotenuse = AB / AC = 8 / 17

Tangent (tan) of angle C = Opposite / Adjacent = AB / BC = 8 / 15

Cosine (cos) of angle C = Adjacent / Hypotenuse = BC / AC = 15 / 17

So, the ratios are:

sin C = 8/17

tan C = 8/15

cos C = 15/17

Therefore, the correct options are:

sin C = 8/17

tan C = 8/15

cos C = 15/17

msm555

Answer:

[tex]\sf \sin C = \dfrac{8}{17} [/tex]

[tex]\sf \tan C = \dfrac{8}{15} [/tex]

[tex]\sf \cos C = \dfrac{15}{17} [/tex]

Step-by-step explanation:

To find the trigonometric ratios with respect to angle [tex]\sf C [/tex] in triangle [tex]\sf ABC [/tex], we can use the given side lengths:

  • Opposite side: [tex]\sf AB = 8 [/tex]
  • Adjacent side: [tex]\sf BC = 15 [/tex]
  • Hypotenuse: [tex]\sf AC = 17 [/tex]

Now, let's calculate the trigonometric ratios:

Sine of angle [tex]\sf C [/tex] ([tex]\sf \sin C [/tex]):

[tex]\sf \sin C = \dfrac{\textsf{Opposite}}{\textsf{Hypotenuse}} \\\\= \dfrac{AB}{AC} \\\\= \dfrac{8}{17} [/tex]

Tangent of angle [tex]\sf C [/tex] ([tex]\sf \tan C [/tex]):

[tex]\sf \tan C = \dfrac{\textsf{Opposite}}{\textsf{Adjacent}} \\\\= \dfrac{AB}{BC} \\\\= \dfrac{8}{15} [/tex]

Cosine of angle [tex]\sf C [/tex] ([tex]\sf \cos C [/tex]):

[tex]\sf \cos C = \dfrac{\textsf{Adjacent}}{\textsf{Hypotenuse}} \\\\= \dfrac{BC}{AC} \\\\= \dfrac{15}{17} [/tex]

Therefore, the trigonometric ratios with respect to angle [tex]\sf C [/tex] in triangle [tex]\sf ABC [/tex] are:

  • [tex]\sf \sin C = \dfrac{8}{17} [/tex]
  • [tex]\sf \tan C = \dfrac{8}{15} [/tex]
  • [tex]\sf \cos C = \dfrac{15}{17} [/tex]

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