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
vladimir1956 [14]
3 years ago
5

The figure above shows a right-angled triangle OAB. AOC is a minor sector enclosed in the triangle. If OA = 7 cm, AB = 6 cm, cal

culate the area and perimeternof the shaded region.​ PLEASE HELP!

Mathematics
1 answer:
dolphi86 [110]3 years ago
7 0

Answer:

Step-by-step explanation:

Given that:

OA = 7 cm, AB = 6 cm. ∠A = 90°, OA = OC = 7 cm

Using Pythagoras theorem: OB² = OA² + AB²

OB² = 6² + 7²=85

OB = √85 = 9.22 cm

to find ∠O, we use sine rule:

\frac{AB}{sin(O)}=\frac{OB}{sin(A)}\\  \\sin(O)=\frac{AB*sin(A)}{OB}=\frac{6*sin(90)}{9.22} =0.65 \\\\O=sin^{-1}0.65=40.6^o

AOC is a minor sector with radius 7 cm and angle 40.6

The Area of the triangle OAB = 1/2 × base × height = 1/2 × OA × AB = 1/2 × 7 × 6 = 21 cm²

Area of sector OAC = \frac{\theta}{360}*\pi r^2=\frac{40.6}{360}*\pi *7^2=17.37 \ cm^2

Area of shaded region = The Area of the triangle OAB - Area of sector OAC = 21 - 17.37 = 3.63 cm²

Perimeter of arc AC = \frac{\theta}{360}*2\pi r=\frac{40.6}{360}*2\pi *7=4.96\ cm

CB = OB - OC = 9.22 - 7 = 2.22

Perimeter of shaded region = AB + CB + arc AC = 6 + 2.22 + 4.96 = 13.18 cm

You might be interested in
Tell me everything I need to know and please work out the problems
ankoles [38]

Answer:

okay so the first one ull need to kno pemdas so start with the perenthesis (5^2-10) and then the exponent 2^3 and multyply thats by 5 and what ever answer u got in the perenthisis u divide by what u got with the second side of the problem

Step-by-step explanation:

if u need more help ill tutor u on it :)

7 0
3 years ago
Read 2 more answers
What is an equation of the line that passes through the points (6, 4) and (4,1)?
netineya [11]

Answer:

3/2 x-5

Step-by-step explanation:

7 0
3 years ago
Read 2 more answers
The product of 15 and the sum of a number and 5 expression
Sedbober [7]
(15)(x+5) because product means multiply the two terms tigether
7 0
3 years ago
What is the slope of the line?<br> y +3 = -4(x+7)
Svetach [21]

Answer:

  -4

Step-by-step explanation:

Compare this to the form ...

  y -y1 = m(x -x1)

which is the point-slope form of the equation for a line. Matching the parts of the equation, you see that ...

  • y1 = -3
  • m = -4
  • x1 = -7

m represents the slope of the line. The slope is -4.

8 0
3 years ago
Read 2 more answers
What value of b makes the polynomial below a perfect square?
Mademuasel [1]
The best and most correct answer among the choices provided by your question is the second choice or letter B. 12

Substituting b = 12:

x^2 + 12x + 36 = (x + 6) ( X + 6) ; therefore, a perfect square.

I hope my answer has come to your help. Thank you for posting your question here in Brainly. We hope to answer more of your questions and inquiries soon. Have a nice day ahead!
8 0
3 years ago
Read 2 more answers
Other questions:
  • steven wants to buy a $500 bicycle steven has no money saved but will be able to deposit $45 into a savings account when he rece
    13·1 answer
  • Is 4/5 greater then 0.75
    10·2 answers
  • Polynomials are written with the exponents of the terms in _____ order.
    10·2 answers
  • Oil is leaking from a tanker at the rate of R(t) = 2000e^(-0.2t) gallons per hour where t is measured in hours. How much oil lea
    9·1 answer
  • Jimmy, Joe and sally are racing their cars. Jimmy and Joe have completed the same number of laps- six fewer laps than Sally. If
    11·1 answer
  • True or False: All statements of equality below are correct. Please help!!
    7·1 answer
  • There are 5 people at a party. They decide to share 3 ice cream sandwiches equally.
    13·1 answer
  • A farmer uses a grain bin which is made up of a cone on top and a cylinder at the
    10·1 answer
  • Help due soon <br> find the area using 3.14 for π<br> round to the nearest Hundredth if you have too
    15·1 answer
  • What is the equation of the line?
    6·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!