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
Triss [41]
3 years ago
13

For positive acute angles A and B, it is known that tan A = 35/12 and sin B = 20/29. Find the value of sin(A - B ) in the simple

st form.
Mathematics
1 answer:
almond37 [142]3 years ago
6 0

Answer:

\displaystyle \sin(A-B)=\frac{495}{1073}

Step-by-step explanation:

We are given that:

\displaystyle \tan(A)=\frac{35}{12}\text{ and } \sin(B)=\frac{20}{29}

Where both A and B are positive acute angles.

And we want to find he value of sin(A-B).

Using the first ratio, we can conclude that the opposite side is 35 and the adjacent side is 12.

Then by the Pythagorean Theorem, the hypotenuse is:

h = \sqrt{35^2 + 12^2} =37

Using the second ratio, we can likewise conclude that the opposite side is 20 and the hypotenuse is 29.

Then by the Pythagorean Theorem, the adjacent is:

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

Therefore, we can conclude that:

So, for A, the adjacent is 12, opposite is 35, and the hypotenuse is 37.

For B, the adjacent is 21, opposite is 20, and the hypotenuse is 29.

We can rewrite sin(A-B) as:

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

Using the above conclusions, this yields: (Note that since A and B are positive acute angles, all resulting ratios will be positive.)

\displaystyle \sin(A-B)=\Big(\frac{35}{37}\Big)\Big(\frac{21}{29}\Big)-\Big(\frac{12}{37}\Big)\Big(\frac{20}{29}\Big)

Evaluate:

\displaystyle \sin(A-B)=\frac{735-240}{1073}=\frac{495}{1073}

You might be interested in
Could someone please help me i really don't understand this
Ray Of Light [21]

Answer:

69

Step-by-step explanation:

8 0
3 years ago
Read 2 more answers
The table shows values for functions f(x) and g(x) .
sladkih [1.3K]
The first thing we must do for this case is to equal both functions and clear the value of x. Thus, we obtain the values that satisfy both equations.
 However, there is another solution route. We have a table with the values.
 The solution for f (x) = g (x) will be all x satisfying both equations simultaneously.
 f (0) = g (0) = 1
 f (1) = g (1) = 1/2
 answer
 x = 0
 x = 1
 Note:
 F (0) in the table is incorrect if the function is
 f (x) = 0.5x
 F (0) in the table is correct if the function is
 f (x) = 0.5 ^ x
5 0
3 years ago
Lin notices that the number of cups of red paint is always 15 of the total number of cups (0.2 of the total number of cups). She
ivann1987 [24]

Step-by-step explanation:

The number of cups of red paint is always 15 of the total number of cups. 0.2 of the total number of cups.

She writes the equation r = 15t (r = 0.2t) to describe the relationship.

In this case, the total no. of cups is an independent variable. No. of cups do not depend on any term.

The number of cups of red paint is a dependent variable as it depends on the number of cups.

7 0
2 years ago
A math textbook has 6 pages of instruction for every 2 pages of practice problems. How many pages of instruction does it have fo
gayaneshka [121]

Answer:

Unit rate is found simply by dividing.

6 pages of instruction/2 pages of practice problems = 3 pages of instruction per page of practice problems

Step-by-step explanation:

6 0
3 years ago
Read 2 more answers
Jack uses a probability simulator to roll a six-sided number cube 100 times and to flip a coin 100 times. The results of the exp
Mandarinka [93]

The experimental probability is the number of specific outcomes divided by the sample size...


P(6)=27/100  (27%)


P(H)=41/100  (41%)


Not sure, but if you meant rolling a 6 AND getting a head then:


P(6 AND H)=(27/100)(41/100)=1107/10000  (11.07%)




5 0
3 years ago
Read 2 more answers
Other questions:
  • The following phrase is an algebraic expression. Use Z for the unknown.
    5·1 answer
  • I need help with number 7
    10·2 answers
  • Evalute <img src="https://tex.z-dn.net/?f=%20sin%5E2%28%5Cfrac%7B%5Cpi%7D%7B12%7D%29%20" id="TexFormula1" title=" sin^2(\frac{\p
    13·1 answer
  • Surface area of composite objects
    7·1 answer
  • Order the temperatures from greatest to least.
    8·1 answer
  • Convert.<br> 1,000 grams =<br> kilograms
    11·2 answers
  • What are the coordinates of the vertex for f(x) = 3x2 + 6x + 3? (−1, 0) (3, 6) (0, −1) (6, 3)
    10·2 answers
  • Colin invests £4300 into his bank account.
    10·1 answer
  • The wheels on Kevin’s bike have a diameter of about 3 feet. How far does the bike travel in 12 complete rotations? (Use 3.14 to
    14·2 answers
  • The length of a rectangle is 5 less than twice the width, and the area of the rectangle is 52 ft^2. Find the dimensions of the r
    12·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!