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
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]
