Chord length

  • MHB
  • Thread starter karush
  • Start date
  • #1
karush
Gold Member
MHB
3,267
4
View attachment 8904

Ok this should be just an observation solution ..
But isn't the equation for chord length
$$2r\sin{\frac{\theta}{2}}=
\textit{chord length}$$

Don't see any of the options
Derived from that..
 

Attachments

  • 20190315_092610.jpg
    20190315_092610.jpg
    7.3 KB · Views: 40

Answers and Replies

  • #2
Olinguito
239
0
Hi karush.

All the information is there. You just need to calculate the angle $\theta$ from the arc length $s=r\theta$.
 
  • #3
karush
Gold Member
MHB
3,267
4
Hi karush.

All the information is there. You just need to calculate the angle $\theta$ from the arc length $s=r\theta$.

It is asking for chord lenght!
 
  • #4
MarkFL
Gold Member
MHB
13,302
7
I would start with the arc-length formula to find the subtended angle:

\(\displaystyle \theta=\frac{s}{r}=\frac{3.4}{2}=1.7\)

Then, use the law of cosines:

\(\displaystyle \overline{DF}=\sqrt{2^2+2^2-2(2)(2)\cos(1.7)}=2\sqrt{2-2\cos(1.7)}\)

Lastly, a double-angle identity for cosine:

\(\displaystyle \overline{DF}=2\sqrt{4\sin^2(0.85)}=4\sin(0.85)\)
 
  • #5
karush
Gold Member
MHB
3,267
4
Ok
So that's where .85 comes from
So then it's D
 
  • #6
Olinguito
239
0
It is asking for chord lenght!

And to do that, you need to know the angle $\theta$, don’t you? Calculate that first!
 
  • #7
karush
Gold Member
MHB
3,267
4
Why of course we do!

However for this SAT question
It is only asking which
Expression to use
We should know that 1.7 is not the $\theta$ we need
and we have use sin $\theta$
So even without any calculations we should see that it is D
 
Last edited:
  • #8
Olinguito
239
0
You were asking
Don't see any of the options
That was because you were given arc length $s=3.4$ (and radius $r=2$) but not $\theta$. I was therefore instructing you to compute $\theta$ from the formula $s=r\theta$ so you could use it in the formula $2r\sin\dfrac{\theta}2$ for the chord length.
 

Suggested for: Chord length

Replies
0
Views
865
Replies
4
Views
827
  • Last Post
Replies
7
Views
7K
Replies
13
Views
1K
  • Last Post
Replies
1
Views
283
Replies
12
Views
696
Replies
8
Views
333
Replies
1
Views
392
Replies
17
Views
570
Top