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3 years ago

How should I solve for x and what is x?

Mathematics

1 answer:

algol [13]3 years ago

8 0

Answer:

x =12

Step-by-step explanation:

We can use the Pythagorean theorem to solve for x

a^2 + b^2 = c^2

16^2 + x^2 = 20^2

256 +x^2 = 400

Subtract 256 from each side

256-256 +x^2 = 400-256

x^2 =144

Take the square root of each side

sqrt(x^2) =sqrt(144)

x = 12

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Step-by-step explanation:

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2 years ago

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Explanation:

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Note that both sine and cosine are negative because x is in the 3rd quadrant.

Recall the addition identities listed below:

$\sin(\alpha + \beta) = \sin\alpha\sin\beta + \cos\alpha\cos\beta$

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$\cos(\alpha - \beta) = \cos\alpha \cos\beta + \sin\alpha \sin\beta$

$\Rightarrow \cos(180 - x) = \cos180\cos x + \sin180\sin x$

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$\tan(\alpha - \beta) = \dfrac{\tan\alpha - \tan\beta}{1 + \tan\alpha\tan\beta}$

$\Rightarrow \tan(360 - x) = \dfrac{\tan 360 - \tan x}{1 + \tan 360 \tan x}$

$\;\;\;\;\;\;= -\tan x = -\dfrac{5}{12}$

Therefore, the expression reduces to

$\sin(180+x) + \tan(360-x) + \frac{1}{\cos(180-x)}$

$\;\;\;\;\;= \left(\dfrac{5}{13}\right) + \left(\dfrac{5}{12}\right) + \dfrac{1}{\left(\frac{12}{13}\right)}$

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2 years ago

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algol [13]

C)
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3 years ago

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