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]
1 year ago
12

A triangle is inscribed in a circle. The vertices of the triangle divide the circle into three arcs of lengths 3, 4, and 5. What

is the area of the triangle
Mathematics
1 answer:
krok68 [10]1 year ago
5 0

The area of the required triangle is <u>9/π²(3  + √3)</u> sq. units.

In the question, we are given that a triangle is inscribed in a circle. The vertices of the triangle divide the circle into three arcs of lengths 3, 4, and 5.

We are asked for the area of the triangle.

Now, the circumference of the circle = 3 + 4 + 5 = 12 units.

The formula for the circumference is 2πr, which gives is:

2πr = 12,

or, r = 6/π.

The length of the arcs are proportional to its central angle, making the angles: 3θ, 4θ, and 5θ, which needs to sum up to 360°, giving us θ = 360°/12 = 30°.

Thus, the three arcs subtends angles of θ₁ = 3θ = 90°,θ₂ = 4θ = 120°, and θ₃ = 5θ = 150°.

The area of the circle can be calculated as:

Area = (1/2)r² sin θ₁ + (1/2)r² sin θ₂ + (1/2)r² sin θ₃ = r²/2(sin θ₁ + sin θ₂ + sin θ₃).

Substituting the values, we get:

Area = 36/2π²(sin 90° + sin 120° + sin 150°),

or, Area = 36/2π²( 1 + √3/2 + 1/2),

or, Area = 9/π²(3  + √3).

Thus, the area of the required triangle is <u>9/π²(3  + √3)</u> sq. units.

Learn more about a triangle at

brainly.com/question/13734546

#SPJ4

You might be interested in
If Carbon 12 is named 12 because it has 6 protons
tester [92]

Answer:

6

Step-by-step explanation:

8 0
2 years ago
Find the volume of a cone with a radius of 8 cm and height 15 cm? Round to the nearest tenth. Please show work.
Nonamiya [84]
You multiply radius by 3.14 by the height  if you plug it in your equation is 8×3.14×15 which equals 1005.31 which rounds to 1005, the answer is 1005! :D
4 0
2 years ago
What’s the area and perimeter for this problem?
notka56 [123]

Answer:

the area of the triangle is 41

the perimiter of the triangle is 33.25

Step-by-step explanation:

4 0
2 years ago
12 + r = 3 <br> how do i solve this?
antoniya [11.8K]
You’d have to try to get r on one side of the equation.
You can do that by subtracting 12 from both sides which would make it so
R = -9
5 0
2 years ago
Read 2 more answers
The reminder when the square of any prime number greater than 3 is divided by 6 is ​
tresset_1 [31]

Answer:

(A) 1(B) 3 (C) 2(D) 4

Step-by-step explanation:

7 0
3 years ago
Other questions:
  • Someone PLEASE help me find the answer
    5·1 answer
  • Which equation, in point-slope form, represents a line with m= -4/7 that goes through the point (-1, 4)?
    6·1 answer
  • a box contains 'n' quarters and some dimes. the ratio of quarters to dimes is 1:2. write an expression for the total number of m
    5·1 answer
  • What is an<br> equation of the line that passes through the points (-4, 4) and (8,1)?
    5·2 answers
  • HURRY PLEASE
    6·2 answers
  • I need super help on this . I’m doing a quiz right now .
    8·1 answer
  • Can someone please explain
    10·1 answer
  • Elisa used 4 cups of flour to
    5·1 answer
  • There are 15 boys in school base ball team , they represent 5% of grace Christian school , In all how many are there in school
    6·1 answer
  • Sub to oiVJDF NvlC Nvlkjxdv Nlkj;zsdn
    6·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!