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"Match each trigonometric value or vocabulary word with its formula or right triangle definition. Use the triangle below."
1. (a/c)
2. (b/c)
3. (opposite/hypotenuse)
4. (adjacent/hypotenuse)
5. (a/b)
6. (b/a)

a. sin B
b. cosine
c. tan B
d. sin A
e. tan A
f. sine

picture involved refresh if not visible Match each trigonometric value or vocabulary word with its formula or right triangle definition Use the triangle below 1 class=

Respuesta :

1. (a/c)
= (opposite/hypotenuse A)
= sin A (d)

2. (b/c)
= (opposite/hypotenuse B)
= sin B (a)

3. (opposite/hypotenuse)
= sine (f)

4. (adjacent/hypotenuse)
= cosine (b)

5. (a/b)
= (opposite/adjacent A)
= tan A (e)

6. (b/a)
= (opposite/adjacent B)
= tan B (c)

hope it helps!

Answer:

1 =d

2=a

3=f

4=b

5=e

6=c

Step-by-step explanation:

We are given a right angled triangle ABC

AB =  c

BC =  a

AC =  b

Using Trigonometric ratio:

[tex]Sin\theta = \frac{Perpendicular}{Hypotenuse}[/tex]

[tex]Sin\theta = \frac{BC}{AB}[/tex]

For perpendicular BC base angle for sine is ∠A

So, [tex]Sin A = \frac{a}{c}[/tex]

So, 1 = d

Using Trigonometric ratio:

[tex]Sin\theta = \frac{Perpendicular}{Hypotenuse}[/tex]

[tex]Sin\theta = \frac{opposite}{Hypotenuse}[/tex]   --1

[tex]Sin\theta = \frac{AC}{AB}[/tex]

For perpendicular AC base angle for sine is ∠B

So, [tex]Sin B = \frac{b}{c}[/tex]

So, 2 = a

Using 1

[tex]Sin\theta = \frac{opposite}{Hypotenuse}[/tex]

So, 3 = f

[tex]Cos \theta = \frac{Base}{Hypotenuse}[/tex]

[tex]Cos \theta = \frac{Adjacent}{Hypotenuse}[/tex]

So, 4 = b

Using Trigonometric ratio:

[tex]Tan\theta = \frac{Perpendicular}{Base}[/tex]

[tex]Tan\theta = \frac{BC}{AC}[/tex]

For Base AC base angle for Tan is ∠A

So, [tex]tan A = \frac{a}{b}[/tex]

So, 5 = e

Using Trigonometric ratio:

[tex]Tan\theta = \frac{Perpendicular}{Base}[/tex]

[tex]Tan \theta = \frac{AC}{BC}[/tex]

For Base BC base angle for Tan is ∠B

So, [tex]tan B = \frac{b}{a}[/tex]

So, 6 = c

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