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
Bingel [31]
3 years ago
6

For positive acute angles A and B, it is known that cos A= 20/29 and tan B= 11/60. Find the value of cos(A + B) in simplest form

.
Mathematics
1 answer:
jek_recluse [69]3 years ago
3 0

Answer:

\displaystyle \cos(A + B) =\frac{969}{1769}

Step-by-step explanation:

We are given that:

\displaystyle \cos A=\frac{20}{29}\text{ and } \tan B=\frac{11}{60}

Where A and B are positive acute angles.

And we want to find cos(A + B).

Recall that cosine is the ratio of the adjacent side to the hypotenuse. Using this information, find the opposite side with respect to Angle A:

o=\sqrt{29^2-20^2}=21

Tangent is the ratio of the opposite side to the adjacent side. Find the hypotenuse with respect to Angle B:

h=\sqrt{11^2+60^2}=61

In summary:

With respect to Angle A, the adjacent side is 20, opposite is 21, and the hypotenuse is 29.

With respect to Angle B, the adjacent side is 60, the opposite is 11, and the hypotenuse is 61.

We can rewrite our expression as:

\displaystyle \cos(A+B)=\cos A\cos B-\sin A\sin B

Using the above information, substitute in the appropriate values. Note that since A and B are positive acute angles, all trigonometric values will be positive. Hence:

\displaystyle \cos(A + B)=\left(\frac{20}{29}\right)\left(\frac{60}{61}\right)-\left(\frac{21}{29}\right)\left(\frac{11}{61}\right)

Simplify:

\displaystyle \cos(A + B) =\frac{1200-231}{1769}=\frac{969}{1769}

You might be interested in
What is the 8th term of this sequence 2,8,18,36,66, 112,178
hjlf
〖〗Fonts for iPhone & Android - www.fontskeyboard.com〖〗Fonts for iPhone & Android - www.fontskeyboard.com〖〗Fonts for iPhone & Android - www.fontskeyboard.com〖〗Fonts for iPhone & Android - www.fontskeyboard.com〖〗Fonts for iPhone & Android - www.fontskeyboard.com〖〗Fonts for iPhone & Android - www.fontskeyboard.com〖〗Fonts for iPhone & Android - www.fontskeyboard.com〖〗Fonts for iPhone & Android - www.fontskeyboard.com〖〗Fonts for iPhone & Android - www.fontskeyboard.com 〖〗Fonts for iPhone & Android - www.fontskeyboard.com〖〗Fonts for iPhone & Android - www.fontskeyboard.com〖〗Fonts for iPhone & Android - www.fontskeyboard.com〖〗Fonts for iPhone & Android - www.fontskeyboard.com〖〗Fonts for iPhone & Android - www.fontskeyboard.com〖〗Fonts for iPhone & Android - www.fontskeyboard.com〖〗Fonts for iPhone & Android - www.fontskeyboard.com
6 0
3 years ago
What is the value of the 1 in 178
Igoryamba
The value of 1 in 178 is 100 since it is in the hundreds place.  The value of 7 in 178 is 70 and the value of 8 in 178 is 8.  The hundreds place carries numbers from 1 to 9.  Once you get to 10, you add a digit to the number such that you now have four total numbers and the first digit is in the thousands place.
3 0
3 years ago
Plz plz help I will get you points :---/
ladessa [460]
I would think it would be B
5 0
3 years ago
Read 2 more answers
A jar contains 18 apple lollipops, 7 strawberry lollipops, and 10 grape lollipops. Irvin randomly selects a lollipop, gives it t
andrey2020 [161]
First  choice is  "1 of 10 grape lollipops from 35 lollipops"  
The probablity is 10/35 = 2/7 
Second choice is  "1 of 18 apple lollipops from 34 lollipops"  
So probablity is 18/34 = 9/17 
Between this is  AND so you have to these probablities multiply:
P(A) = 2/7 * 9/17 = 18/119 
P(A) = 18/119 * 100% = 1800/119 %
It is approximaly 15,1 %. 
4 0
3 years ago
Read 2 more answers
RV=y+27 and TV=3y–17, find RV in parallelogram RSTU.<br> T<br> S<br> R<br> U<br> V
zaharov [31]

Answer:

RV = 49 units

Step-by-step explanation:

in parallelogram RSTU , the diagonals bisect each other, then

TV = RV , that is

3y - 17 = y + 27 ( subtract y from both sides )

2y - 17 = 27 ( add 17 to both sides )

2y = 44 ( divide both sides by 2 )

y = 22

Then

RV = y + 27 = 22 + 27 = 49 units

6 0
2 years ago
Other questions:
  • At a New Car Dealership a particular model comes in 4 trims levels, 5 different colors, and 3 different interiors. How many diff
    7·1 answer
  • The perimeter of the isosceles triangle to the right is 35 inches. what is the value of x
    11·1 answer
  • Create a problem where the answer to the problem is your birthday. Make sure you use the Order of Operations. My B-Day is 4.
    11·1 answer
  • Cal is measuring temperature changes in four substances over different time periods as part of a school project. Which data show
    10·1 answer
  • A baseball player got 102 hits in the last 300 times at bat. Explain how you would find the percent of times the baseball player
    7·2 answers
  • Mary decided to buy the yellow rose bush for $7.89. Tax was 55 cents. What was the total price including tax?
    14·2 answers
  • Find the equation of the line. Use exact numbers
    9·1 answer
  • Which of the following statements best explains why this graph represents a relation that is not a
    15·2 answers
  • PLEASE HELP IF YOU CAN! IM DESPERATE! DUE TODAY!
    7·2 answers
  • Can you please help me?​
    11·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!