Question

FAN + MEDAL!!!
If AC = 5 cm, BC = 12 cm, and measure of arc AC=40degrees, the radius of the circumscribed circle is _______cm and measure of angle OAC=______degrees

https://cdn.ple.platoweb.com/EdAssets/e1a63a1350b3409bb29cd96ddf440e30?ts=635385680875800000

Answer 1

@deprix

Answer 2

Please copy down this diagram if you haven't already. Mark every known (e. g., mark sides AC and BC and angle B). Because this triangle is drawn inside a half circle, it's a right triangle; Angle C is 90 degrees.

How would you find the length of BC?

Answer 3

length of BC is given in the question, which is 12cm

Answer 4

What's the length of side AC? What method would you use the find the length of side AB?

Answer 5

length of AC = 5cm.
pythagorean theorem or trig?

Answer 6

As I said before, triangle ABC is a right triangle. Use that fact and the lengths of sides AC and BC to find the length of side AB.

Answer 7

okay are you sure its a right triangle? it wasnt given

Answer 8

can i use pythagorean theorem?

Answer 9

Because this triangle is drawn inside a half circle, it's a right triangle; Angle C is 90 degrees. But you're within your rights to want justification for this.

Yes, you may use the Pyth. Thm.

Answer 10

I got 13 for length of side AB

Answer 11

There is a theorem in geometry that states that if a triangle is inscribed in HALF of a circle, the angle opposite the hypotenuse of the cicle (which is also its diameter) is 90 degrees.

13 is correct. Now, what's the radius of the circle?

Answer 12

so radius would be half of 13, which is 6.5

Answer 13

and okay awesome i didnt know that

Answer 14

Perfect. Now, what's the other question alrady posted here?

Answer 15

measure of angle OAC = ________?

Answer 16

Yes. How would you go about finding the measure of angle OAC?

Answer 17

Triangle degrees add up to 180. this is a right triangle so its either
45.45.90
or
30.60.90

Answer 18

But that's a special case. What if one of the acute angles were 44 degrees and the other 46 degrees?

Answer 19

im not sure how to find the answer. does it involve trig

Answer 20

Yes, it does. All three sides of the triangle are now known. Which of the basic three trig functions could you use to find the measure of angle OAC?

Answer 21

tan?

Answer 22

I used the tan function, yes. you could also use the sine or cosine. Up to you! But the answer, the measure of angle OAC, must be the same no matter which method you use.

Answer 23

okay i need help setting up what to enter into the calculater

Answer 24

I'd rather you write out the formula you're using on paper or type it in here. Once we're OK with that, we can find the actual angle using your calculator.

Answer 25

tan(θ) = Opposite / Adjacent

Answer 26

Yes. How does that apply here?

Answer 27

tan(θ) = 12 / 5

Answer 28

Fine. You could also use sin theta =12/13.

What kind of calc have you?

Answer 29

TI-84 Plus Silver Edition

Answer 30

Great. We want to find the measure of angle OAC. Since we don't know that measure yet, the tan function won't help here. What we use, instead, is the inverse tan function. Have you used that before?

Answer 31

yes i have

Answer 32

trig confuses me

Answer 33

then pull up the inv. tan. fn. and use the argument 12/5.

Answer 34

Press 2nd, tan. Then type in 12/5). press enter.

Answer 35

I got 1.176

Answer 36

Looks as tho your calculator is in RADIAN mode. Can you set it to DEGREE mode? Press the MODE key next to the 2nd key.

Answer 37

oh yeah i forgot about that

Answer 38

67.38 so thats the angle measure of OAC?

Answer 39

Yes. great job. rounding that off to 2 decimal places was also a good move.

Answer 40

thanks very much!

Answer 41

my great pleasure! take care.