Question

Can someone help me solve for the smaller segment of a circle. chord 3sqr2 and angle is 90 degrees

Answer 1

Do you have a picture ?

Answer 2

and exactly what is the question ?

Answer 3

yes,

Answer 4

is it like this?

Answer 5

yes that's the picture

Answer 6

and exactly what is the question ?

Answer 7

find the area of the smaller segmebt of the cicle. round your answer to two decimal points

Answer 8

First, you need to find the radius. Notice you have a right angle so you have a right triangle
do you know the pythagorean theorem ?

Answer 9

c=asq2 + bsqr2

Answer 10

yes, now to use that formula we have to label the triangle's sides.
we can label its legs "r" (for radius) because both legs are a radius.
what is c (hypotenuse) in our triangle ?

Answer 11

3sqr2

Answer 12

ok. we should tweak your version of pythagoras
it is
\[ c^2 = a^2 + b^2 \]
to use it , replace c with \(3 \sqrt{2} \)
replace a with r
replace b with r
can you do that ?

Answer 13

ok, i did that and equation is 18=rsqr2+rsqr2

Answer 14

yes
if you use the equation editor it looks nicer
\[ 18 = r^2 + r^2 \]

if you have 1 r squared and add another r squared how many r^2 do we have ?

Answer 15

2

Answer 16

which means
\[ 18 = r^2 + r^2 \]
simplifies to
\[ 18 = 2r^2 \]
can you solve for r ?
The next step is divide both sides by 2

Answer 17

r=3

Answer 18

The next step is
what is the formula for the area of a circle ?

Answer 19

\[pirsq\]

Answer 20

A = pi r^2 (use ^ to show 2 is an exponent)

so the area of the whole circle is
A= pi * 3^2 = 9 pi

Answer 21

ok thank u

Answer 22

next, the "sector" is what fraction of the circle ?

Answer 23

if the whole circle is a pie, the sector is what fraction of the whole pie ?

Answer 24

can you guess ?

Answer 25

1/4