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
How many triangles are shown, including any overlapping triangles?
olga55 [171]
8 triangles in the image 
4 0
3 years ago
Read 2 more answers
Identify any restrictions on the variable.
Wittaler [7]

Answer:

x=mc2 + 86

Step-by-step explanation:

4 0
2 years ago
Find the slope of a line parallel to y=(2/5)x + (4/5)
Tcecarenko [31]

Answer:

So if a line was parallel it would have same slope. You can search up what slope-intercept form means. But if you have an equation like this:

y = mx+b

The slope will be m. Your question is written in the form. 2/5 = m.

The slope is 2/5

The y-intercept is 4/5

6 0
2 years ago
Read 2 more answers
con 16 barras de mantequilla se prepararon 20 postres ?que fraccion del total de mantequilla corresponde a cada postre
MatroZZZ [7]

De ahí que la fracción de la mantequilla total que corresponde a cada postre sea 1/4

Si con 16 barras de mantequilla se prepararon 20 postres, esto se puede expresar como:

16 pegatinas = 20 postres

Para obtener la fracción del total de mantequilla que corresponde a cada postre, podemos escribir;

x = 1 postre

Divide ambas expresiones

16 / x = 20/1

20 veces = 16 * 1

20x = 16

x = 16/20

x = 4/5

De ahí que la fracción de la mantequilla total que corresponde a cada postre sea 1/4

Obtenga más información aquí: brainly.com/question/1878884

5 0
2 years ago
At Costco, you can buy a ten-pound bag of Halloween candy for $23.99. Kroger is running a special on the same brand of candy: bu
kirill [66]

Answer:

A. 2.40

B. 4

C. Costco is the better deal

Step-by-step explanation:

23.99/10= 2.399 (rounded to 2.40)

10/2.5 lbs (16 oz = 1 lb) = 4

6 0
3 years ago
Other questions:
  • What is the simpliest form of 121/16
    10·2 answers
  • What is the ratio of course to cups in a carton of milk
    13·1 answer
  • Please anwer what is X and give the explantion,how did you get the answer.ASAP
    9·2 answers
  • Justin earned 8 badges in Scouts. Justin wants to complete 2 more badges so that he will have a total of 10 badges. If Justin co
    8·1 answer
  • HELP PLEASE ASAP!!!!
    7·1 answer
  • What is 4.238 x 7.5.​
    7·1 answer
  • Equation equal to z^-1 divided by 3
    9·1 answer
  • Find the circumference of the pizza. Round your answer to the nearest hundredth.
    7·1 answer
  • I feel real d.umb for asking this much of questions but tbh I don’t like algebra, my math teacher doesn't like me and she never
    11·1 answer
  • A database contains 58,000 items. Items are added to the database at a rate of 2 items per minute.
    8·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!