1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
MAXImum [283]
2 years ago
13

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

nd the value of \cos(A+B)cos(A+B) in simplest form.
Mathematics
1 answer:
MrRa [10]2 years ago
7 0

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}

You might be interested in
Another algebra problem i cant solve
zhenek [66]

Answer:

where is the problem?

Step-by-step explanation:

6 0
3 years ago
I NEED HHELP ASAP STOP SENDING ME LINK
Ymorist [56]

Answer:

The answer is B

Step-by-step explanation:

hope that helps

5 0
3 years ago
Read 2 more answers
Aubrey’s monthly bank statement shows a total of $51 in fees for ATM withdrawals. If Audrey made 17 withdraws, what is Audrey ch
Tpy6a [65]

Answer:

Audrey was charged $3 for each withdrawal.

Step-by-step explanation:

We have to calculate the amount of money charged on one transaction.

In order to find the amount for one ATM withdrawal, the total amount for ATM withdrawals will be divided by number of withdrawals.

Given

Total\ ATM\ withdrawal\ fees = \$51\\Total\ withdrawals = 17\\Amount\ for\ one\ withdrawal = \frac{Total\ fees}{No.\ of\ withdrawals}\\= \frac{51}{17}\\= \$3

Hence,

Audrey was charged $3 for each withdrawal.

7 0
3 years ago
In the diagram below, PQ and RS are parallel. Based on the angle measures in the diagram, what is the value of X?
Butoxors [25]

Answer:

x would be equal to 70 grades

Step-by-step explanation:

The angle QRS is equal to 180 - 130 = 50 grades.

We add up that with the other 60 grades on the left, and we encounter ourselves with a simple equation:

60 + x + 50 = 180

x = 70

Hope this was helpful

4 0
2 years ago
In 2007, the U.S. population was 302 million people. In 2012, it was 314 million. What was the rate of population change per yea
allsm [11]

Answer:

314/302=1.039735 growth in US population in 5 years

(1.039735)^1/5=0.782% average growth in US population per year.

6 0
3 years ago
Other questions:
  • Do I multiply and add?
    9·1 answer
  • Explain the differences between adding and multiplying radical expressions using 2 examples you create.
    13·1 answer
  • The endpoints of a line segment are at the coordinates (–6, 3, 4) and (4, –1, 2). What is the midpoint of the segment?
    13·1 answer
  • Partial product of 8.6x9.2
    6·1 answer
  • I need help on this question
    11·2 answers
  • ....!!!.I need help!!!
    8·1 answer
  • Find the area of the composite figure.
    14·2 answers
  • Question 8 of 10<br> Simplify (7 + 1)2 – (11 + 32) - 4.
    5·1 answer
  • 0.15 + 0.1x = 1.1 ÷ 3 · 5.1 − 1.2
    10·1 answer
  • New to Geometry! Help me pls!
    12·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!