torialaw89
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Look at the figure:

An image of a right triangle is shown with an angle labeled x.

If tan x° = a divided by 4 and cos x° = 4 divided by b what is the value of sin x°?

sin x° = 4b
sin x° = b divided by a
sin x° = 4a
sin x° = a divided by b

I believe it's A or C

Look at the figure An image of a right triangle is shown with an angle labeled x If tan x a divided by 4 and cos x 4 divided by b what is the value of sin x si class=

Respuesta :

Banabanana
If tan(x) = a/4, then a is opposite to the angle x and 4 is adjacent to the angle x

If cos(x) = 4/b, then 4 is adjacent to the angle x and b is the hypotenuse

sin(x) =  opposite/hypotenuse = a/b

Answer is D.
Ver imagen Banabanana
kudzordzifrancis
ANSWER

[tex] \sin(x) = \frac{a}{b} [/tex]


EXPLANATION

It was given that,

[tex] \tan(x) = \frac{a}{4} [/tex]



and

[tex] \cos(x) = \frac{4}{b} [/tex]


We can use the relation,

[tex] \tan(x) = \frac{ \sin(x) }{ \cos(x) } [/tex]


This implies that,


[tex] \cos(x) \times \tan(x) = \sin(x) [/tex]





We now substitute the given values to get,


[tex] \frac{a}{4} \times \frac{4}{b} = \sin(x) [/tex]

[tex] \sin(x) = \frac{a}{b} [/tex]


Or

Since

[tex] \tan(x) = \frac{a}{4} = \frac{opposite}{adjacent} [/tex]


It means the length of the opposite side is
[tex]a \: units[/tex]


and the length of the adjacent side is
[tex]4 \: units[/tex]


Also,

[tex] \cos(x) = \frac{4}{b} = \frac{adjacent}{hypotenuse} [/tex]


This also means that, the hypotenuse is
[tex]b \: units[/tex]



But
[tex] \sin(x) = \frac{opposite}{hypotenuse} [/tex]


This implies that,


[tex] \sin(x) = \frac{a}{b} [/tex]


The correct answer is D.

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