Question

1. In the diagram below, line segment AT is a diameter of the circle with center O. What is the area of the shaded part of the circle? Show your work or provide an explanation for your answer.

Answer 1

can someone help me?

Answer 2

I'm not really good with this stuff sorry D:

Answer 3

its okay..

Answer 4

@touseii45

Answer 5

okay well you want to find the area of the circle first

Answer 6

so do you know your formula?

Answer 7

the area is 201.1

Answer 8

OK, first find the area of the circle, which is \[\pi \times r ^{2}\] and r is half of the diameter

Next find the area of the triangle. To do that, calculate the base and the height, using the fact that u know the hypothenuse and the angle 30. Than use the formula :
area of a triangle=0.5xheightxbase

Answer 9

now youve lost me :(

Answer 10

what he means is 3.14 (which is pi) times r squared (or half of the diameter times itself)

Answer 11

i know the area of the circle

Answer 12

if your diameter is 16 divide that by 2

Answer 13

what is it?

Answer 14

the area is 201.1

Answer 15

correct now do you have the area of the triangle?

Answer 16

no, i cant figure out how..

Answer 17

ok, do u know that sinx=opposite/hypothenuse ?

Answer 18

and that cosx=adjacent/hypothenuse?
u can use these two facts to find the base and the height of the triangle

Answer 19

im sorry thanks for your help, but im more confused than before i cane here

Answer 20

im confused too

Answer 21

did u learn about sine and cosine? If u haven't, than I don't see how u could solve this question

Answer 22

yes.

Answer 23

alittle

Answer 24

so what exactly do i do to find the area of the triangle

Answer 25

OK, so \[\sin (of an \angle)=\frac{side opposite \to \angle }{ hypothenuse (the longest side of the \triangle }\]

Answer 26

and
\[\cos x=\frac{ adjacent }{ hypothenuse }\]

Answer 27

but which fdo i do?

Answer 28

you throwing formulas at me is just confusing me

Answer 29

therefore, to find the base of the triangle, we calculate:
\[\sin(30)=\frac{ base }{ 16 }\]
and to find the height of the triangle, we calculate:
\[\cos (30)=\frac{ height }{ 16 }\]

Answer 30

I'm sorry, I'm not trying to confuse, I'm just working through the problem with u

Answer 31

oohhhh okay!!1

Answer 32

we got it?

Answer 33

:D

Answer 34

but how do i solve them?

Answer 35

well,
\[the base=16\sin 30\]
\[the height=16\cos 30\]

Answer 36

so?

8 and 13.86

Answer 37

ok, now we plug that into the triangle fornmula (which is half times base times height)
And then we subtract the area of the triangle from that of the circle

Answer 38

55.44 and 201.1-5544=145.66

os that right?

Answer 39

55.44***

Answer 40

:D well done! that's what i got, anyways

Answer 41

so final answer=145.636304

Answer 42

:)