Question

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​

Answer 1

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 2

Answer:

$\sf \sin C = \dfrac{8}{17}$

$\sf \tan C = \dfrac{8}{15}$

$\sf \cos C = \dfrac{15}{17}$

Step-by-step explanation:

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

• Opposite side: $\sf AB = 8$
• Adjacent side: $\sf BC = 15$
• Hypotenuse: $\sf AC = 17$

Now, let's calculate the trigonometric ratios:

Sine of angle $\sf C$ ($\sf \sin C$):

$\sf \sin C = \dfrac{\textsf{Opposite}}{\textsf{Hypotenuse}} \\\\= \dfrac{AB}{AC} \\\\= \dfrac{8}{17}$

Tangent of angle $\sf C$ ($\sf \tan C$):

$\sf \tan C = \dfrac{\textsf{Opposite}}{\textsf{Adjacent}} \\\\= \dfrac{AB}{BC} \\\\= \dfrac{8}{15}$

Cosine of angle $\sf C$ ($\sf \cos C$):

$\sf \cos C = \dfrac{\textsf{Adjacent}}{\textsf{Hypotenuse}} \\\\= \dfrac{BC}{AC} \\\\= \dfrac{15}{17}$

Therefore, the trigonometric ratios with respect to angle $\sf C$ in triangle $\sf ABC$ are:

• $\sf \sin C = \dfrac{8}{17}$
• $\sf \tan C = \dfrac{8}{15}$
• $\sf \cos C = \dfrac{15}{17}$