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
valkas [14]
3 years ago
11

Calculate area and perimeter​

Mathematics
1 answer:
mina [271]3 years ago
5 0

Answer:

area ≈ 12.505

perimeter ≈  16.1684

Step-by-step explanation:

We are given

- the radius of the circle (and therefore area of the circle)

- the area of the triangle

We want to find

- angle AOB/AOT. We want to find this because 360/the angle gives us how many OABs fit into the circle. For example, if AOT was 30 degrees, 360/30 = 12 (there are 360 degrees in a circle, so that's where 360 comes from). The area of the circle is equal to πr² = π6² = 36π, and because AOT is 30 degrees, there are 12 equal parts of sector OAB in the circle, so 36π/12=3π would be the area of the sector. A similar conclusion can be reached from the circumference instead of the area to find the distance between A and B along the circle, and OA + AB + BO = the perimeter of the minor sector.

First, we can say that OAT is a right triangle because a tangent line is perpendicular to the line from the center to the point on the circle, so AT is perpendicular to OA. This forms two right angles, one of which is OAT

One thing that we can start to solve is AT. We know that the area of a triangle is equal to base * height /2, and the height of this triangle is AO, with the base being AT. Therefore, we can say

15 = AO * AT / 2

15 = 6 * AT / 2

15 = 3 * AT

divide both sides by 3 to isolate AT

AT = 5

Because OAT is a right triangle, we can say that the hypotenuse ² =  the sum of the squares of the two other lengths. The hypotenuse is opposite of the largest angle (in this case, the right angle, as in a right triangle, the right angle is always the largest), so it is OT in this case. The other two sides are OA and AT, so we can say that

OA² + AT² = OT²

5²+6² = OT²

25+36=61=OT²

square root both sides

OT = √61

Next, the Law of Sines states that

sinA/a = sinB/b = sinC/c with angles A, B, and C with sides a, b, and c. Corresponding sides are opposite their corresponding angles, so in this case, AT corresponds to angle AOT, OT corresponds to angle OAT, and AO corresponds to angle ATO.

We want to find angle AOT, as stated earlier, so we have

sin(OAT)/OT = sin(ATO)/OA = sin(AOT)/AT

We know the side lengths as well as OAT/sin(OAT) and want to figure out AOT/sin(AOT), so one equation that helps us get there is

sin(OAT)/OT = sin(AOT)/AT, encompassing our 3 known values and isolating the one unknown. We thus have

sin(90)/√61 = sin(AOT) /5

plug in sin(90) = 1

1/√61 = sin(AOT)/5

multiply both sides by 5 to isolate sin(AOT)

5/√61 = sin(AOT)

we can thus say that

arcsin(5/√61) = AOT ≈39.80557

As stated previously, given ∠AOT, we can find the area and perimeter of the sector. There are 360/39.80557 ≈ 9.04396 equal parts of sector OAB in the circle. The area of the circle is πr² = 36π, so 36π / 9.04396 ≈ 12.505 as the area. The circumference is equal to π * diameter = π * 2 * radius = 12 * π, and there are 9.04396 equal parts of arc AB in the circumference, so the length of arc is 12π / 9.04396 ≈ 4.1684. Add that to OA and OB (both are equal to the radius of 6, as any point from the center to a point on the circle is equal to the radius) to get 6+6 + 4.1684 = 16.1684 as the perimeter of the sector

You might be interested in
Find the value please help me
Lemur [1.5K]
The answer is 318

Hope this helps

3 0
3 years ago
Read 2 more answers
Pls help will give the big brain award <br><br> +if you help more you get more brainliest
Effectus [21]
64 in2 is the answer
7 0
3 years ago
Read 2 more answers
Find the unknown measure of the rectangle.<br> Area =28 square centimeters <br>Height =?
taurus [48]
Area of rectangle = Length*width
A = 28  so 28 = 4 * height
height  = 28/4 = 7
6 0
3 years ago
Read 2 more answers
Tammy baked a batch of 20 cupcakes. Daniella baked
ElenaW [278]

Multiplication is the process of multiplying. The total number of cupcakes that are produced by the 3 girls is 44.

<h3>What is multiplication?</h3>

Multiplication is the process of multiplying, therefore, adding a number to itself for the number of times stated. For example, 3 × 4 means 3 is added to itself 4 times, and vice versa for the other number.

Given that Tammy baked a batch of 20 cupcakes and Daniella baked 4/5 as many cupcakes as Tammy. Therefore, the number of cupcakes made by Daniella is,

Number of cupcakes made by Daniella

= (4/5)×(Number of cupcakes made by Tammy)

= (4/5) × 20

= 16

Now, if Miko baked 1/2 as many cupcakes as Daniella. Therefore, the number of cupcakes made by Miko is,

Number of cupcakes made by Miko

= (1/2) × (Number of cupcakes made by Daniella)

= (1/2) × 16

= 8

Further, the total number of cupcakes that are produced are,

Number of cupcakes = 20 + 16 + 8 = 44

Hence, the total number of cupcakes that are produced by the 3 girls is 44.

Learn more about Multiplication here:

brainly.com/question/14059007

#SPJ1

8 0
1 year ago
I need help it's due tomorrow​
hoa [83]

5 and 4

3 and 6

hope this helps!

4 0
3 years ago
Read 2 more answers
Other questions:
  • In the given figure, what is the measure of angle CPE?
    6·1 answer
  • the walls of a square room need painting.Each of the four walls is 12 ft wide by 8.5 feet tall.One gallon of paint covers 75 ft.
    11·2 answers
  • Whats the difference between adding me on ig <br><br> answer papi_lopez_4k<br> help me reach 100
    5·2 answers
  • The last week of a month a car dealership sold 12 cars. A new sales promotion came out the first week of the next month and the
    14·1 answer
  • Prove the Converse of the Pythagorean Theorem using similar triangles. The Converse of the Pythagorean Theorem states that when
    8·1 answer
  • SMART PEOPLES HELP ME
    5·1 answer
  • PLZ HELP I NEED THIS TODAY! Choices are:
    7·2 answers
  • I need help on this one.
    13·1 answer
  • Hewo do u know fractions because I am dying from it T-T<br><br> 1/2+___=7/6<br><br> Help T-T
    11·1 answer
  • A cuboid with a breadth of 4 cm and length of 6 cm has a volume of 350 cm3. Find the height of the cuboid, giving you answer to
    6·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!