Question

What is the length of DB?

https://media.glynlyon.com/g_geo_2012/13/img_geou13a_49.gif

2
2
2 square root 3
square root 3
1.5

Answer 1

Do you know how to find CD?

Answer 2

no ):

Answer 3

Do you know trig?

Answer 4

yes!

Answer 5

Ok. Remember this.
SOH-CAH-TOA

Answer 6

\[\sin \theta = \frac{ Opp }{ Hyp }\]
\[\cos \theta = \frac{ Adj }{ Hyp. }\]
\[\tan \theta = \frac{ Opp }{ Adj }\]

Answer 7

You see where I got SOHCAHTOA now?

Answer 8

yes!

Answer 9

Ok. So, we're going to solve for CD now. We're given the angle 30 degrees and the Hypotenuse of triangle ACD. CD is OPPOSITE of the angle given.
The hypotenuse equals 6.
\[\cos30 = \frac{ CD }{ 6 }\]
so

\[CD = 6\cos(30)\]

cos(30) =
\[\sqrt(3)/2\]
So.
CD = 3sqrt(3)

Answer 10

Does this make sense?

Answer 11

OOPS!

Answer 12

yes it does!

Answer 13

wait...

Answer 14

use sin! Not cos!

Answer 15

ye yea!! i was looking at that one more time too! haha

Answer 16

sin(30) = 1/2

Answer 17

so CD = 3

Answer 18

because CD = 6sin(30)

Answer 19

sorry!

Answer 20

so would it be
square root of 3??

Answer 21

these are the answers!

2
2 square root 3
square root 3
1.5

Answer 22

Hang on.

Answer 23

I'm going to draw what we've just done.

Answer 24

We have found CD. Now we have to find that angle and use trig once more to find DB

Answer 25

Do you know how we would find that angle?

Answer 26

would it be 45 degrees since it was a 90 degrees before spliting in half?

Answer 27

Remember that the sum of all angles in a triangle is 180. In triangle ACD, we have one angle that is 90 degrees and another angle that is 30 degrees.
90+30+angle(ACD) = 180
This means that angle ACD would be 60 degrees right?

Answer 28

yess

Answer 29

But we want DCB

Answer 30

Do you know what DCB is now?

Answer 31

It's just ACD subtracted by 90 right?

Answer 32

or 90 subtracted by ACD. :p

Answer 33

90-60 = 30

Answer 34

Does this all make sense?

Answer 35

Now we have.