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
Alexxx [7]
3 years ago
13

For positive acute angles A and B, it is know that tan A= 8/15 and sin B= 11/61. Find the value of cos (a+b) in simplest form

Mathematics
1 answer:
iragen [17]3 years ago
7 0

Answer:

812/1037

Step-by-step explanation:

To solve this, we have to use trigonometric identities.

Cos (A + B) is given as Cos A Cos B - Sin A Sin B. And from the question, we have that

Tan A = 8/15.

We know that in a triangle, the Tan angle is represented Opp/Adj and thus the Opp is 8, and the Adj is 15. Using Pythagoras, we have

hyp² = opp² + adj²

hyp² = 8² + 15²

hyp² = 64 + 225

hyp² = 289

hyp = √289 = 17

The identity of Cos is Adj/Hyp and that of Sin is Opp/Hyp.

Cos A = 15/17

Sin A = 8/17

Repeating the same process for B, we have

Sin B = 11/61

adj² = hyp² - opp²

adj² = 61² - 11²

adj² = 3721 - 121

adj² = 3600

adj = √3600 = 60

Cos B = 60/61

Now, using the earlier stated trigonometric identity, we have

cos (a + b) = CosA CosB - SinA SinB

cos (a + b) = 15/17 * 60/61 - 8/17 * 11/61

cos (a + b) = 900/1037 - 88/1037

cos (a + b) = 812/1037

You might be interested in
Thirty-five percent of what number is 10.5?
erastovalidia [21]

30% of 35 = 10.5

35 would be your answer. 

3 0
3 years ago
Read 2 more answers
A circle has a diameter of 24 units. Find the circumference and area of the circle in terms of π.
enyata [817]
Circumference=24 pi
Area=144 pi, shown clearly in photo

7 0
3 years ago
Read 2 more answers
A cube shaped pool is half full of water. If the water is 36 inches deep, how much would the water in the pool weigh if the pool
solmaris [256]
36 inches = half the depth of the pool , so depth of pool = 72 inches = 6 ft
Volume of the cube = 6^3 = 216 cu ft
weight of the water = 216 * 56 pounds
  =   12096 pounds
5 0
3 years ago
Element X is a radioactive isotope such that every 90 years, its mass decreases by half. Given that the initial mass of a sample
steposvetlana [31]

Answer:

approximately 27 grams

Work Shown:

Half life formula

y = A*(0.5)^(x/H)

where,

A = starting amount = 30 grams

H = half life period = 90 years

x = number of years that pass by = 12

y = amount left over after x years

Let's plug the values for x, A and H into the formula to find y

y = A*(0.5)^(x/H)

y = 30*(0.5)^(12/90)

y = 27.3516746567466

y = 27 .... rounding to the nearest whole number

4 0
3 years ago
Name four angles between 0 and 360 degrees with a reference angle of 20 degrees Show work
Archy [21]
20, 180 - 20, 180 + 20 and 360 - 20

i.e. 20°, 160°, 200° and 340°
5 0
3 years ago
Read 2 more answers
Other questions:
  • Write the equation of the circle in general form. Show all of your work
    11·2 answers
  • Part A. At the local baker you can get 10 cookies for $2. How many cookies could you get for $5 dollars?
    11·1 answer
  • The function f is defined by f(x)=-x2+2x-7. What is the value of f(-3)?
    9·1 answer
  • If you are given multiple choice question test, what is the odds of guessing wrong?
    11·2 answers
  • How do you find x and y in a word problem
    9·1 answer
  • What is the answer to this ?
    15·2 answers
  • 2,11,20 find the t15
    6·1 answer
  • Help me ASAP please really quick it’s my last question <br><br> Find the area of this please
    12·2 answers
  • NEED ANWSERS 16-21 FAST
    9·1 answer
  • A landscape business charges $50 to deliver rocks. The cost of the rocks are $27 per cubic yard. write and solve a linear equati
    13·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!