Check my answer??? I think the answer is true! Question is attached below!

Question

anonymous · Answer

attachment

anonymous · Answer

This question was fun, it's part of the unit b test right?

anonymous · Answer

@iambatman Nah, it was on a quiz for me... It's driving me crazy though

anonymous · Answer

Ah, well what was your attempt?

anonymous · Answer

wow, how would you work this out?
my guess is that theta is about 49.11 degrees

I dont know if it's cheating, but I think you need to draw two circles at 7cm apart, and then measure the triangles formed by the intersect.

anonymous · Answer

or the angles of the intersect

anonymous · Answer

@iambatman I got that theta was 22.5, but I'm not sure it it's right?? Thoughts

@hughfuve I never knew that trick! Is there a formula to use to check if the 49.11 is right??

anonymous · Answer

@ganeshie8 sorry to bother ya, but could ya help? The question is attached on the first reply!

ganeshie8 · Answer

use `law of cosines` : http://www.mathwarehouse.com/trigonometry/images/law-of-cosines/law-of-cosines-formula-and-picture2.png

ganeshie8 · Answer

$$\large 5.3^2 = 4^2 + 7^2 - 2(4)(7)\cos(\theta)$$

ganeshie8 · Answer

find the value of $\large \cos (\theta)$ first

anonymous · Answer

So, my result would be 5.32=114-56cos(theta)???

ganeshie8 · Answer

$$\large 5.3^2 = 4^2 + 7^2 - 2(4)(7)\cos(\theta)$$

$$\large \cos(\theta) = \dfrac{4^2 + 7^2 -5.3^2}{ 2(4)(7)}$$

anonymous · Answer

Oh!!! So it'd equal -35.016???

ganeshie8 · Answer

http://www.wolframalpha.com/input/?i=%284%5E2+%2B+7%5E2+-+5.3%5E2%29%2F%282%284%29%287%29%29

ganeshie8 · Answer

$$\large \cos(\theta) = \dfrac{4^2 + 7^2 -5.3^2}{ 2(4)(7)} = 0.659$$

$$\large \implies \theta =  \arccos(0.659) =  48.77^{\circ}$$

anonymous · Answer

Argh... Okay. I see it now. Gosh it's still confusing, but at least now I have an example problem so thank you :)

ganeshie8 · Answer

@hughfuve  is right ! his method looks interesting :)

anonymous · Answer

I like your method better.. that is awesome.. @ganeshie8

ganeshie8 · Answer

:) to solve these type of problems, you need to know only two formulas : 1) law of sines 2) law of cosines go thru these short videos once @mathisfun1283 https://www.khanacademy.org/math/trigonometry/less-basic-trigonometry/law-sines-cosines/v/law-of-cosines-example

anonymous · Answer

Thank you!! I love khan academy! :)