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Answer:

See Below

Step-by-step explanation:

Tan is the ratio of "opposite" side to "adjacent side

Cos is the ratio of "adjacent" to "hypotenuse"

Sin is the ratio of "opposite" to "hypotenuse"

We will write the trig ratios with respect to the angle "x"

Opposite Side is "c"

Adjacent Side is "b"

Hypotenuse is the side opposite of 90 degree angle, "a"

Now, let's write the ratios:

[tex]Sin \ x =\frac{c}{a}\\Cos \ x = \frac{b}{a}\\Tan \ x = \frac{c}{b}[/tex]

The required value of the trigonometrical ratios are,

[tex]tanx=\frac{b}{c}[/tex]

[tex]cosx=\frac{c}{a} \\\\sinx=\frac{b}{a}[/tex]

To understand the calculations, check below

Trigonometrical ratios:

Trigonometric ratios are the ratios of sides of a right-angle triangle. The most common trigonometric ratios are sine, cosine, and tangent.

GIven lengths are

Perpendicular=[tex]b[/tex]

Hypoteneous=[tex]a[/tex]

Base=[tex]c[/tex]

Now, calculating the trigonometrical ratios as,

[tex]tanx=\frac{perpendicular}{base}=\frac{b}{c}[/tex]

[tex]cosx=\frac{base}{hypotenuse}=\frac{c}{a} \\sinx=\frac{perpendicular}{hypotenuse}=\frac{b}{a}[/tex]

Learn more about the topic of trigonometrical ratios:

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