Question

Find the area of the shaded region enclosed in a semicircle of diameter 8 centimeters. The length of the chord AB is 6 centimeters. Answer to 2 decimal places. (Hint: Triangle ABC is a right triangle.) put in cm^2

http://www.webassign.net/sat/10-4-29.gif

Answer 1

Several ways to this, higher math use double integrals polar. However, it could be done geometrically. Calculate the area of the triangle; calculate area of semi-circle; Subtract

Answer 2

this one right?

Answer 3

yup

Answer 4

ah, thats such a pretty picture lol

Answer 5

haha lol. its 3am and im doin maths lol. thats commiitment haha

Answer 6

diam = 8; radius = 4

the area of each 'segment' = area sector - area triangle

Answer 7

lets get the larger angle; using law of cos; in a good way lol

6^2 = 4^2 + 4^2 - 2(4)(4) cos(C)

36 - 16 - 16
----------- = cosC; C = cos^-1 of that stuff right?
-32

Answer 8

36 - 32 = 4

-4
--- = -1/8
32

Answer 9

haha looks good

Answer 10

-1/8 ill giv it a try

Answer 11

151.04 is what i get in degrees lol

Answer 12

2.636 rads i think

Answer 13

hahaha. so im guessin the -1/8 is in cm^2 ?

Answer 14

..... maybe :)

Answer 15

hahahaha

Answer 16

there is a simpler way.... my other personality just was sitting there laughing at me and finally told me this..

Answer 17

since the radius = 4; what is the area of the half cirlce?

pi r^2
----- right?
2

Answer 18

righto

Answer 19

8pi total area of the half....

Answer 20

subtract area of the tri now

Answer 21

ohh i see. and area of tri is found by cos formula right?

Answer 22

or vectors :)

Answer 23

but yeah

Answer 24

how do u use vectors

Answer 25

draw lines with arrows attached

Answer 26

lets go with law of cosines to figure angles tho

Answer 27

area triangle (1/2)bh

Answer 28

to find the height we gotta know an angle

Answer 29

Height is given, right triangle.

Answer 30

cos^(-1)[-1/8] gives us an inside angle of what... 115.yada right?

Answer 31

151.04497562814015224245793040175 i meant lol

Answer 32

180 - angle
---------- = angle we can use
2

Answer 33

i got 97.180

Answer 34

14.477512 is the angle onthe left side

Answer 35

6 sin(angle) = height

Answer 36

kinda lost me there

Answer 37

the interior angle at the center there is abt 151 right?

Answer 38

ye i was gettin about 97.18 instead of the 151

Answer 39

we got an isosoleces triangle

so the other 2 angles are the same right?

180 - 151
--------- = angle we need
2

Answer 40

why do i get dofferent result lol

Answer 41

it is -1/8 right?

Answer 42

lol not sure but is it cos(^-1)(-1/8) ?

Answer 43

yeah,, the -1/8 part cud be the mess up

Answer 44

6^2 = 4^2+4^2 -2(4)(4) cosC

36 - 32
------- = 4/-32 = -1/8
-32

Answer 45

nah it cant be then

Answer 46

cos^-1(-1/8) = abt. 97

Answer 47

yes thats the one

Answer 48

it must be my fat fingers gettin gin the way lol

Answer 49

hahaha its all good

Answer 50

180 - 97.180755781458281323038995626149
--------
2

Answer 51

41.409622109270859338480502186926

now we got this angle we can determine the height by its sin times that 6 distance

Answer 52

3.968... is what I get for height

Answer 53

h*8
--- = area of tri
2

Answer 54

lol for the height i got -0.92

Answer 55

15.8745 = area tri

now subtract that from the area of the hemicircle

Answer 56

lol.... do it again

Answer 57

so u did Sin(41.40*6) for height?

Answer 58

8pi - 15.8745.... = 9.258....

Answer 59

the 6 is outside

Answer 60

6 sin(angle)

Answer 61

ohhh

Answer 62

okah so its 9.258 cm^2

Answer 63

thats what i get; but then again.... i am just an idiot in disguise ;)

Answer 64

lol as if. u answered so many of my q's!!!

Answer 65

and wallah its correct!!

Answer 66

yay!!

Answer 67

double yay!!!