Question

The circle in the figure has a radius of r and center at C. The distance from A to B is x, the distance from A to D is y, and the length of arc BD is s. Redraw the figure, label it as indicated, and solve the problem.

If A = 29°, s = 12, and r = 14, find x.

Answer 1

is this for trig?

Answer 2

@jdoe0001 yes

Answer 3

notice in the triangle given, you're given the arc, that is the central angle of 12 degrees andd the angle A of 29 degrees
the obtuse angle will be 180-(29+12) = 139 degrees

Answer 4

$$\bf {
\text{using law of sines}\\
\cfrac{12}{sin(29^o)} = \cfrac{14+x}{sin(139^o)}\\
\cfrac{12\times sin(139^o)}{sin(29^o)} = 14+x\\
x = \cfrac{12\times sin(139^o)}{sin(29^o)} -14
}
$$

Answer 5

hmm

Answer 6

darn! I have a typo :/

Answer 7

the opposite side to 29 degrees is 14 :/, not 12

Answer 8

thus
$$\bf {
\text{using law of sines}\\
\cfrac{14}{sin(29^o)} = \cfrac{14+x}{sin(139^o)}\\
\cfrac{14\times sin(139^o)}{sin(29^o)} = 14+x\\
x = \cfrac{14\times sin(139^o)}{sin(29^o)} -14
}
$$

Answer 9

@jdoe0001 Okay, I think I understand thank you!

Answer 10

yw

Answer 11

@jdoe0001 I tried it & the answer is wrong :/ am I supposed to add it to something?

Answer 12

no

Answer 13

retry the calculation, keep in mind you're using Degrees, no Radians
so make sure your calculator is in Degrees mode

Answer 14

I get -0.68

Answer 15

hmmm wait a minute, that' make no sense hehe

Answer 16

Oh, I got 5. aha & then for the picture, since s = 12. Would I use s = r * theta to find the central angle of C.

Answer 17

meh, I forgot to close a parentheses, anyhow, yes is 5 rounded up

Answer 18

hmm, "s" is given pretty much, "s" is 12 degrees

Answer 19

Even though 's' is the arc length?