Express answer in exact form. A segment of a circle has a 120 arc and a chord of 8in. Find the area of the segment.
1 answer:
Answer:
13.09 in²
Step-by-step explanation:
<u>Formula to find the Area of Segment:</u>
- <em>A= (θ × π/360° − sin(θ)/2) × r², where θ = arc in degrees, r = radius of circle</em>
<em>We need to find the radius of the circle for our calculation of area of the segment.</em>
<em>Refer to picture.</em>
<u>The right triangle ΔOBC has:</u>
- BC= 1/2 of chord AB = 8 in/2 = 4 in
- ∠COB = 1/2 θ= 1/2*120° = 60°
<u>Since ΔOBC is 30-60-90 triangle:</u>
<u>Then the area of segment:</u>
- A= (θ × π/360° − sin(θ)/2) × r² =
- (120° × π/360° − sin(120°)/2) × (8√3/3)² =
- (3.14/3 - √3/4)× 64/3 =
- 13.09 in²
<u>Answer:</u> 13.09 in²
You might be interested in
Answer:
x = −2
Step-by-step explanation:
the steps are super long but this is the answer
9514 1404 393
Answer:
2/3
Step-by-step explanation:
The scale factor is the ratio of corresponding dimensions:
(6 cm)/(9 cm) = 2/3
Answer:
1)Coefficient
2)Dividend
3) Quotient
Step-by-step explanation:
Answer:
answer is 1
Step-by-step explanation:
You want to do 209/11 and get 19 as your answer