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
Rainbow [258]
3 years ago
7

How do you solve this problem?

Mathematics
1 answer:
jekas [21]3 years ago
3 0
Very nice problem. You should look up the history of this question. It has a very long one having to do with mirrors made between 50 BC and 50 AD.

Step One
Find AB, BC, AC
Before beginning this problem, I'm going to arbitrarily name 
c = AB
a = BC
b = AC It just makes the calculations easier.

AB = radius of the large circle - radius of the medium circle = 20.62 - 8.04 = 12.58
BC = Radii of the two smaller circles added together = 8.04 + 7.35 = 15.39
AC = Radius of the large circle - Radius of the small circle = 20.62 - 7.35 = 13.27

So
a = 15.39
b = 13.27
c = 12.58

Step Two
Find Angle A or <BAC
a^2 = b^2 + c^2 - 2*b*c * Cos(A)
15.39^2 = 12.58^2 + 13.27^2 - 2 * 12.58 * 13.27 * Cos(A)
236.852 = 158.26 + 176.1 -  333.87 * Cos(A)
236.852 = 334.4 - 333.87*Cos(A)
-97.55 = - 333.87 *  Cos(A) 
-97.55 / -333.87 = Cos(A)
0.2922 = cos(A)
A = cos-1(0.2922)
A = 73.01 degrees

Step Three
Just to see if you understand what was done, I'll give you the givens for finding c, and the answer and you can work through the calculations to see if your answer agrees with mine. If it doesn't PM me.
c = 12.58
b = 13.27
a = 15.39

12.58^2 = 13.27^2 + 15.39^2 - 2*13.27*15.39*Cos(C)
C = 51.42

Step Four
Find <B
Every triangle has 180 degrees so
B = 180 - <A - C
B = 180 - 51.42 - 74.01
B = <54.57. 
I have found a moderator who opened the question up so that I can show you why the Cos law is the only way to do this. If the circles are very disproportionate as in this diagram, then no simple assumption can be made. The cos law is all that will work. I would have posted this earlier, but I didn't think anyone would find another method. It's ingenious but not possible for the situation below.

You might be interested in
June bought ​ 3 1 2 312 ​ gallons of white paint at $17.50 per gallon and ​ 1 3 4 134 ​gallons of blue paint at $19.00 per gallo
algol [13]
312* 17.5= 5460.00

134*19=2546

2546+5460= $8,006.00
5 0
3 years ago
Glenn rode his bike for 2 hours
Natali5045456 [20]
Cool. I rode mine for 1.
5 0
2 years ago
Read 2 more answers
What is the absolute value of 9.8 and
Citrus2011 [14]
The answer is -10/3 your answer
7 0
3 years ago
The height of a cylinder is 5 centimeters. The diameter of the base of the cylinder is 16 centimeters. Find the lateral surface
soldier1979 [14.2K]

Answer:

Lateral surface area of the cylinder =251.2 cm^2

Step-by-step explanation:

  Lateral surface area of he cylinder = 2*\pi*r*h  i.e area of side surface.

Height(h) = 5 cm

Diameter = 16 cm

radius(r)= 16/2= 8 cm

Lateral surface area of the cylinder = 2*\pi *8*5                        

                                                                         \pi =\frac{22}{7}=3.14

               L.S.A=  2*3.14*8*5

              L.S.A=  251.2 cm^2

The lateral surface area of the cylinder with radius 8 cm and height 5 cm is 251.2 cm^2

6 0
3 years ago
In the diagram below, If angle 53°,what is the angle of CD​
wel
I need this answer too can someone please help us out with the right answer ?!

Explanation:
8 0
2 years ago
Other questions:
  • Carl deposited $5,142 into a savings account 20 years ago. The account has an interest rate of 3.8% and the balance is currently
    14·1 answer
  • Round 314,759 to the number of the underlined digit
    12·1 answer
  • Then Isabella filled 3 more pages with 36 photos which
    6·1 answer
  • Write -4i+(1/4-5i)-(-3/4+8i)+17i as a complex number in the standard form
    8·1 answer
  • Which of the following tables shows the correct steps to transform x2 + 6x + 8 = 0 into the form (x − p)2 = q? [p and q are inte
    12·1 answer
  • This isosceles triangle has two sides of equal length, a, that are longer than the length of the base, b. The perimeter of the t
    6·1 answer
  • If y varies inversely as x and } = 3 when x = 4, then y
    13·1 answer
  • Someone pls help me ill give out brainliest pls don’t answer if you don’t know
    15·2 answers
  • An agent was able to sell a house and loth worth P2,300,000,00 if he was given a 5% commission.How much did he receive.
    11·1 answer
  • Enter the number 46.1979 rounded to the nearest hundredth (two decimal places)
    6·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!