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3 years ago

If anyone knows it would be helpful

Mathematics

1 answer:

Oduvanchick [21]3 years ago

5 0

Answer:

I believe that the answer is C.

Step-by-step explanation:

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Given the general identity tan X =sin X/cos X , which equation relating the acute angles, A and C, of a right ∆ABC is true?

irakobra [83]

First, note that $m\angle A+m\angle C=90^{\circ}.$ Then

$m\angle A=90^{\circ}-m\angle C \text{ and } m\angle C=90^{\circ}-m\angle A.$

Consider all options:

$\tan A=\dfrac{\sin A}{\sin C}$

By the definition,

$\tan A=\dfrac{BC}{AB},\\ \\\sin A=\dfrac{BC}{AC},\\ \\\sin C=\dfrac{AB}{AC}.$

Now

$\dfrac{\sin A}{\sin C}=\dfrac{\dfrac{BC}{AC}}{\dfrac{AB}{AC}}=\dfrac{BC}{AB}=\tan A.$

Option A is true.

$\cos A=\dfrac{\tan (90^{\circ}-A)}{\sin (90^{\circ}-C)}.$

By the definition,

$\cos A=\dfrac{AB}{AC},\\ \\\tan (90^{\circ}-A)=\dfrac{\sin(90^{\circ}-A)}{\cos(90^{\circ}-A)}=\dfrac{\sin C}{\cos C}=\dfrac{\dfrac{AB}{AC}}{\dfrac{BC}{AC}}=\dfrac{AB}{BC},\\ \\\sin (90^{\circ}-C)=\sin A=\dfrac{BC}{AC}.$

Then

$\dfrac{\tan (90^{\circ}-A)}{\sin (90^{\circ}-C)}=\dfrac{\dfrac{AB}{BC}}{\dfrac{BC}{AC}}=\dfrac{AB\cdot AC}{BC^2}\neq \dfrac{AB}{AC}.$

Option B is false.

$\sin C = \dfrac{\cos A}{\tan C}.$

By the definition,

$\sin C=\dfrac{AB}{AC},\\ \\\cos A=\dfrac{AB}{AC},\\ \\\tan C=\dfrac{AB}{BC}.$

Now

$\dfrac{\cos A}{\tan C}=\dfrac{\dfrac{AB}{AC}}{\dfrac{AB}{BC}}=\dfrac{BC}{AC}\neq \sin C.$

Option C is false.

$\cos A=\tan C.$

By the definition,

$\cos A=\dfrac{AB}{AC},\\ \\\tan C=\dfrac{AB}{BC}.$

As you can see $\cos A\neq \tan C$ and option D is not true.

$\sin C = \dfrac{\cos(90^{\circ}-C)}{\tan A}.$

By the definition,

$\sin C=\dfrac{AB}{AC},\\ \\\cos (90^{\circ}-C)=\cos A=\dfrac{AB}{AC},\\ \\\tan A=\dfrac{BC}{AB}.$

Then

$\dfrac{\cos(90^{\circ}-C)}{\tan A}=\dfrac{\dfrac{AB}{AC}}{\dfrac{BC}{AB}}=\dfrac{AB^2}{AC\cdot BC}\neq \sin C.$

This option is false.

8 0

3 years ago

Read 2 more answers

Jon is taking a 625 mile trip. On the first day, he drove 183 miles.

snow_tiger [21]

Answer:

442

Step-by-step explanation:

625-183=442

6 0

3 years ago

PLEASE HELP :)))

DerKrebs [107]

Answer: 596 + 860 = 1456

5 0

3 years ago

Simplify 12 × 10 ^8/ 4 × 10^5 and leave in ordinary form

Burka [1]

Answer:

3 x 10^3

Step-by-step explanation:

The first is to identify the operation to be performed, it is a quotient between two potency.

Being two potency of the same base number (10), the property says that the quotient of two potency of the same base subtracts its exponent, and the base remains the same.

The corresponding exponents are 8 and 5.

<u>The subtraction is 8-5 = 3</u>.

The whole number that accompanies the base is divided in a current way, that is 12/4. <u>Therefore, the result is 3.</u>

4 0

3 years ago

What is the cost per pencil

belka [17]

Answer:

$0.12/pencil

Step-by-step explanation:

The cost per pencil would be the unit cost or the slope of the given line.

Let's choose the point on the line (200, $24). Note that the graph passes through (0, 0) as well. Then the slope = unit cost per pencil is

m = rise / run = $24/200 pencils = $0.12/pencil

5 0

3 years ago

If anyone knows it would be helpful​

If anyone knows it would be helpful