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Lady_Fox [76]
2 years ago
5

Solve using a paragraph proof

Mathematics
1 answer:
harina [27]2 years ago
4 0

Answer:

you will use the SOHCAHTOA METHOD IF ITS A TRIANGLE. Not sure

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For positive acute angles AA and B,B, it is known that \tan A=\frac{28}{45}tanA= 45 28 ​ and \cos B=\frac{3}{5}.CosB= 5 3 ​ . Fi
MrRa [10]

Answer:

\cos(A + B) = \frac{23}{265}

Step-by-step explanation:

Given

\tan A=\frac{28}{45}

\cos B=\frac{3}{5}

Required

\cos(A+B)

In trigonometry:

\cos(A+B) = \cos\ A\ cosB - sinA\ sinB

We need to solve for cosA, sinA and sinB

Given that:

\tan A=\frac{28}{45} and the tangent of an angle is a ratio of the opposite side (x) to the adjacent side (y),

So, we have:

x =28 and y = 45

For this angle A, we need t calculate its hypotenuse (z).

Using Pythagoras,

z^2 = x^2 + y^2

z = \sqrt{x^2 + y^2

z = \sqrt{28^2 + 45^2

z = \sqrt{2809

z = 53

From here, we can calculate sin and cos A

\sin A= \frac{opposite}{hypotenuse} and \cos A= \frac{adjacent}{hypotenuse}

\sin A= \frac{x}{z}

\sin A= \frac{28}{53}

\cos A= \frac{y}{z}

\cos A= \frac{45}{53}

To angle B.

Give that

\cos B=\frac{3}{5} and the cosine of an angle is a ratio of the adjacent side (a) to the hypotenuse side (c),

So, we have:

a = 3 and b = 5

For this angle B, we need to calculate its opposite (b).

Using Pythagoras,

c^2 = a^2 + b^2

5^2 = 3^2 + b^2

25 = 9 + b^2

Collect like terms

b^2 = 25 - 9

b^2 = 16

b = \sqrt{16

b = 4

From here, we can calculate sin B

\sin B= \frac{opposite}{hypotenuse}

\sin B = \frac{b}{c}

\sin B = \frac{4}{5}

Recall that:

\cos(A+B) = \cos\ A\ cosB - sinA\ sinB

and

\cos B=\frac{3}{5}      \sin B = \frac{4}{5}       \sin A= \frac{28}{53}      \cos A= \frac{45}{53}

\cos(A + B) = \frac{45}{53} * \frac{3}{5} - \frac{28}{53} * \frac{4}{5}

\cos(A + B) = \frac{135}{265} - \frac{112}{265}

\cos(A + B) = \frac{135-112}{265}

\cos(A + B) = \frac{23}{265}

7 0
3 years ago
22. A question bank has questions of Physics and
trasher [3.6K]

Step-by-step explanation:

Let the number of books of Physics be x . Then , No. of chemistry books =3.5x

Now , according to question :

x+3.5x=90

Or , 4.5x=90

Or , x=90/4.5

Or , x=20

Now ,

3.5x= 3.5×20

= 70

Therefore , there were 70 chemistry books and 20 physics books in that question bank.

7 0
2 years ago
Evaluate -4 +(-3) - (-2)
melomori [17]

Answer:

-5

Step-by-step explanation:

-4+(-3)-(-2)

-4-3+2

-7+2

-5

3 0
3 years ago
Read 2 more answers
Please help one of my last questions.....
Shkiper50 [21]

Answer:

B and C

Step-by-step explanation:

Uses my  calculator and put the table in for worker be and thats how i found the slope was 12.5 . then i used to to figure out that when the hour got  to 10 worker B starts making more money.

8 0
3 years ago
D-21.4=87.9 <br> Explain your answer
larisa [96]
<span>D-21.4=87.9 \ solve for D

add 21.4 to both sides
</span><span>D - 21.4 +21.4 =87.9 + 21.4

simplify
D = 109.3</span>
7 0
3 years ago
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