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
12(5+2y)=4y-(6-9y) How to Solve
kvv77 [185]

Answer:

y = -6

Step-by-step explanation:

12 (5 + 2y) = 4y- (6 - 9y)

= 60 + 24y = 4y - 6 + 9y

= 60 + 24y = 13y - 6

= 24y - 13y = -6 - 60

= 11y = -66

y = -6

7 0
3 years ago
Please answer in detail
sammy [17]

Answer:

y=5x-1 I think because the snd option doesn't make sense but you should try y =5x-1

8 0
2 years ago
Aleena expands 2xx+3-5(x-2) as 2x2+3-5x-10. Has she expanded it correctly? Please identify the mistakes and write the correct wa
Nimfa-mama [501]

The given expression is :

2xx+3-5(x-2)

We know that, x{\cdot}x=x^2

=2x^2+3-5(x-2)\\\\=2x^2+3+(-5)(x)+(-5)(-2)\\\\=2x^2+3-5x+10

Aleena expands 2xx+3-5(x-2) as 2x²+3-5x-10. She is mistaken because the sign before 10 should be +10 instead of -10. Hence, the correct expanded form is 2x²+3-5x+10. Hence, this is the required solution.

5 0
2 years ago
Find the volume of the solid. Round to the nearest tenth if necessary.
Vikki [24]
V= \frac{4}{3}  \pi  r^{3} or V=4.1888 r^{3}

r=4 r^{3}=64*4.1888=268.083

V = 268.083 mm^{3} so go with A.

7 0
3 years ago
Malika owns a small business selling bagels. She knows that in the last week 63
Agata [3.3K]
The correct answer is 9/14
8 0
2 years ago
Other questions:
  • What is one way to get permission to use a copyrighted online source? write down the source's publication date locate the owner
    8·2 answers
  • Estimate the quotient 24 3/7÷3 7/13
    11·2 answers
  • An angle of less than 90° is called an.....
    7·2 answers
  • The tempture at 6:00 was 9 degress blow zero. The temperature dropped 11 below zero at 8:00. what is the difference between the
    9·1 answer
  • Combine like terms to simplify the following expressions <br><br> -5a - 4a + b
    9·2 answers
  • Symbol for taken away
    8·2 answers
  • Mr. Kershner is a school nurse. He uses, on average, 24 self-adhesive bandages during each spring month: March, April, and May.
    8·2 answers
  • HELPPPP!!!! A, B, C, or D!
    5·1 answer
  • Two types of tickets are sold to a play. Floor
    7·1 answer
  • Without graphing, determine whether the function represents exponential growth or exponential decay. y=12(17/10)^x
    7·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!