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High school geometry
Challenge problems: Inscribed angles
Solve two challenging problems that apply the inscribed angle theorem to find an arc measure or an arc length.
Problem 1
Problem 2
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Couldn't you have just used the formula S=r*theta ?(15 votes)
Problem 2 : ∠APC = 2 * ∠ABC = 2 * 2/5 π radians = 4/5 π radians
Arc AC = 4/5 π radians * 4 units per radian
= 16/5 π units(13 votes)
In regards to the 2nd problem.
I calculated the "length of AC" to be 7.61... Isn't the term "length of AC" meaning the direct measurement from A to C (forming a triangle APC)? Shouldn't the 2nd problem say, "what is the arc length of AC"?(9 votes)
I don't know if anything's changed since you were here last, but for me it says, "What is the length of AC," and there's a little curve over the letters AC. That means they're talking about arc AC.(20 votes)
couldn't we just transform the radians in degree before using the proportion?(6 votes)
Whenever you convert radians to degrees there will be most likely be rounding involved, meaning the results of your calculations will not be as exact but rather a close approximation.
This means, when you enter the answer it will come up wrong, as it is looking for the exact answer based on the radians, not the approximated answer of degrees.(4 votes)
- just a question of comprehension, in problem 1, using the ratio problem arc length/circumference=arc measure/360, why are you able to shift a denominator dividing a fraction to another number, or in relation to the equation, when you multiply 360 to both sides, and then shift the 24pi under it?(8 votes)
- Hi Joshua,
To answer the "why" part of your question-
Whatever you multiply to one side of the equation, you need to multiply it to the other side of the equation too. When you do so, are are not changing the value of the equation. This helps us to isolate the unknown term (arc measure in this case) to one side of the equation.
So, this is what your equation will look like-
68/15 pi/ 24 pi = arc measure/ 360
we can write the above equation in a simplified form too and it would look like-
68 pi/ 15 X 24 pi = arc measure/ 360
When we multiply both sides by 360, the equation will be-
360 X 68 pi/ 15 X 24 pi = arc measure X 360/ 360 (360/ 360 = 1)
you can see that multiplying by 360 on both sides does not change the equation but will help us to isolate "arc measure" to one side of the equation.
When you simplify, you will get-
360 X 68 pi/ 15 X 24 pi = arc measure
arc measure = 68.
Hope this helps.
Regards,
Aiena.(4 votes)
- shouldn't there be more problems on this stuff?(10 votes)
On the second problem is the angle measure in degrees or radians?(2 votes)
If you see a π in the angle, you can assume it is in radians.(7 votes)
For problem 1, I did it a slightly different way. Instead of saying (68pi/15) = (360degrees/24pi), I divided (68pi/15) by (24pi), and got 1.888.... And then I multiplied that with 360, and got a totally different answer, around 5. How come this yields a totally different answer if its theoretically the same arithmetic action?(2 votes)
When you did: divide (68pi/15) by (24pi, you should have got: 0.188888...
Your decimal point is in the wrong place.
Mulitply by 360: 360 * 0.188888... = 68
Hope this helps.(3 votes)
- Could someone explain to me why [arc length/circumference = arc measure/radians in circle]?(2 votes)
- An arc is a part of the entire circumference, same as an angle, which subtends the arc, is a part of the entire circle, which is 2pi. That is why these ratios are equal.(2 votes)
- How do you get 2 radians?(2 votes)
- In the second question, where did they get 2 pi for radians in a circle?(1 vote)
