The figure below shows a triangular wooden frame ABC. The side AD of the frame has rotted and needs to be replaced:
Triangle ABC has length of BC equal to 16 inches. A line segment DC joins the point D on AB with point C. Measure of angle ABC is 90 degrees, ACD is 15 degrees and measure of angle DCB is 30 degrees.
What is the length of the wood that is needed to replace AD?

- anonymous

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- anonymous

@stacy.reed08

- anonymous

6.8 inches
6.2 inches
3.2 inches
2.8 inches

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- anonymous

I thought maybe doing 15 divided by 2 would work but i got 7.5 inches and thats not an option so im assuming there's a step im missing

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## More answers

- anonymous

I should have looked down at the picture...it took me forever to draw by hand.

- anonymous

ok, so if you think about it, there is a little triangle inside the larger triangle ABC

- anonymous

Yes i see that

- anonymous

ok, let's draw that triangle out separately

- anonymous

|dw:1440107397764:dw|

- anonymous

I take that back...sorry, I thought we were trying to figure out line segment DC...just kidding, we want AD

- anonymous

im guessing in order to find out the rotting piece needed to be replaced we have to find out how long side CD is?

- anonymous

ok, I know the answer and there is probably an easier way to get there, but this is what makes sense in my mind...

- anonymous

use the smaller triangle to figure out the length of DB.

- anonymous

How do we do that

- anonymous

OH

- anonymous

|dw:1440107651617:dw|

- anonymous

ok so BC is 16 inches DB is 30 inches and 180-16-30=134 so Dc is 134

- anonymous

nope, we don't know DB...we know angle DCB is 30 degrees and we know side BC is 16 inches.

- anonymous

but since the angle is 30 degress wouldn't the side across from it be 30 inches?

- anonymous

|dw:1440107798750:dw|

- anonymous

if we pull the little triangle out it's easier to work with

- anonymous

and nope...the side across from it is going to be an ugly number that we'll round a little bit to make it easier to work with.

- anonymous

ok lol

- anonymous

so the missing side x and the angle are related how?

- anonymous

because they're opposite from each other

- anonymous

ok, and how are the angle and the 16 inch side related?

- anonymous

they are adjacent to each other

- anonymous

so you have opposite and adjacent which means what trig function?

- anonymous

Toa= tangent

- anonymous

ok so plug it in and actually solve it out to get a single number. It will be ugly looking so round to 2 digits past the decimal.

- anonymous

How would i solve/calculate this?

- anonymous

Actually one sec

- anonymous

I've gotta grab something off the printer...I'll be back in a minute

- anonymous

Alright

- anonymous

30(tan)16=9?

- anonymous

9.24 just to be a little more accurate

- anonymous

sorry it took so long, I locked my keys in my room and had to go around.

- anonymous

lol it's fine so what would be the answer here then?

- anonymous

the largest option available is 6.8 inches.

- anonymous

or highest rather

- anonymous

ok, so right now you're only part way done...

- anonymous

now let's look at the big triangle...

- anonymous

Lol i just realized

- anonymous

|dw:1440108392044:dw|

- anonymous

so we have the adjacent and opposite again?

- anonymous

yup.

- anonymous

I have to be somewhere at 7 on the dot so in an hour i have to go, just letting you know

- anonymous

And once again i deeply appreciate your patience in helping me solve my geometry problems

- anonymous

So we would do 15(tan)30?

- anonymous

I actually need to leave as soon as we're done with this problem. I'm in grad school and have a paper to write...plus it's past 5 and I'm still at school :(

- anonymous

the angle isn't 30...we need all of angle C

- anonymous

|dw:1440108572263:dw|

- anonymous

ahh so 45, and sorry for taking up so much time lol

- anonymous

you're fine. like I said before, I don't teach math anymore so this is actually fun for me. :) and yes, 45

- anonymous

so what's the length of our missing side?

- anonymous

45?

- anonymous

nope...plug it in just like you did before...your set up was write, just the angle number was wrong. so 16 tan 45

- anonymous

it comes out as 16

- anonymous

yup. so know you know side AB (the entire side) is 16 inches and you know DB is 9.24 so that means AD is ?

- anonymous

or when i put the calculator in Radian form, its 25.9 or 26

- anonymous

oh ok disregard that comment then

- anonymous

the angle was given in degrees so don't use radian form :)

- anonymous

omg 6.76

- anonymous

You are amazing holy christ

- anonymous

i have 3 more answers but with my new found knowledge maybe i can solve them on my own lol

- anonymous

questions not answers*

- anonymous

well I wouldn't go that far...I realized just know that the big triangle ABC is a 45-45-90 triangle which means both legs are equal...

- anonymous

we didn't need to do all that last part....

- anonymous

lol its fine

- anonymous

Do you mind staying for just 3 more questions?

- anonymous

Like just answering them would be fine, as we're both on a time budget, but if you can't then i completely understand.

- anonymous

Unfortunately, I really have to go. The custodian is starting to wonder why I'm still here :)

- anonymous

lol alright see you then thanks for the help and time once again!

- anonymous

no problem! Best of luck on the rest of your problems :)

- anonymous

lol thank you

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