- Thread starter
- #1

#### karush

##### Well-known member

- Jan 31, 2012

- 2,724

- Thread starter karush
- Start date

- Thread starter
- #1

- Jan 31, 2012

- 2,724

- Thread starter
- #3

- Admin
- #4

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

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:

\(\displaystyle \overline{DF}=2\sqrt{4\sin^2(0.85)}=4\sin(0.85)\)

- Thread starter
- #5

- Jan 31, 2012

- 2,724

Ok

So that's where .85 comes from

So then it's D

So that's where .85 comes from

So then it's D

- Apr 22, 2018

- 251

And to do that, you need to know the angle $\theta$, don’t you? Calculate that first!It is asking for chord lenght!

- Thread starter
- #7

- Jan 31, 2012

- 2,724

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

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:

- Apr 22, 2018

- 251

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.Don't see any of the options