anonymous
  • anonymous
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?
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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anonymous
  • anonymous
@stacy.reed08
anonymous
  • anonymous
6.8 inches 6.2 inches 3.2 inches 2.8 inches
anonymous
  • 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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anonymous
  • anonymous
I should have looked down at the picture...it took me forever to draw by hand.
anonymous
  • anonymous
ok, so if you think about it, there is a little triangle inside the larger triangle ABC
anonymous
  • anonymous
Yes i see that
anonymous
  • anonymous
ok, let's draw that triangle out separately
anonymous
  • anonymous
|dw:1440107397764:dw|
anonymous
  • anonymous
I take that back...sorry, I thought we were trying to figure out line segment DC...just kidding, we want AD
anonymous
  • 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
  • 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
  • anonymous
use the smaller triangle to figure out the length of DB.
anonymous
  • anonymous
How do we do that
anonymous
  • anonymous
OH
anonymous
  • anonymous
|dw:1440107651617:dw|
anonymous
  • anonymous
ok so BC is 16 inches DB is 30 inches and 180-16-30=134 so Dc is 134
anonymous
  • anonymous
nope, we don't know DB...we know angle DCB is 30 degrees and we know side BC is 16 inches.
anonymous
  • anonymous
but since the angle is 30 degress wouldn't the side across from it be 30 inches?
anonymous
  • anonymous
|dw:1440107798750:dw|
anonymous
  • anonymous
if we pull the little triangle out it's easier to work with
anonymous
  • 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
  • anonymous
ok lol
anonymous
  • anonymous
so the missing side x and the angle are related how?
anonymous
  • anonymous
because they're opposite from each other
anonymous
  • anonymous
ok, and how are the angle and the 16 inch side related?
anonymous
  • anonymous
they are adjacent to each other
anonymous
  • anonymous
so you have opposite and adjacent which means what trig function?
anonymous
  • anonymous
Toa= tangent
anonymous
  • 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
  • anonymous
How would i solve/calculate this?
anonymous
  • anonymous
Actually one sec
anonymous
  • anonymous
I've gotta grab something off the printer...I'll be back in a minute
anonymous
  • anonymous
Alright
anonymous
  • anonymous
30(tan)16=9?
anonymous
  • anonymous
9.24 just to be a little more accurate
anonymous
  • anonymous
sorry it took so long, I locked my keys in my room and had to go around.
anonymous
  • anonymous
lol it's fine so what would be the answer here then?
anonymous
  • anonymous
the largest option available is 6.8 inches.
anonymous
  • anonymous
or highest rather
anonymous
  • anonymous
ok, so right now you're only part way done...
anonymous
  • anonymous
now let's look at the big triangle...
anonymous
  • anonymous
Lol i just realized
anonymous
  • anonymous
|dw:1440108392044:dw|
anonymous
  • anonymous
so we have the adjacent and opposite again?
anonymous
  • anonymous
yup.
anonymous
  • anonymous
I have to be somewhere at 7 on the dot so in an hour i have to go, just letting you know
anonymous
  • anonymous
And once again i deeply appreciate your patience in helping me solve my geometry problems
anonymous
  • anonymous
So we would do 15(tan)30?
anonymous
  • 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
  • anonymous
the angle isn't 30...we need all of angle C
anonymous
  • anonymous
|dw:1440108572263:dw|
anonymous
  • anonymous
ahh so 45, and sorry for taking up so much time lol
anonymous
  • 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
  • anonymous
so what's the length of our missing side?
anonymous
  • anonymous
45?
anonymous
  • 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
  • anonymous
it comes out as 16
anonymous
  • 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
  • anonymous
or when i put the calculator in Radian form, its 25.9 or 26
anonymous
  • anonymous
oh ok disregard that comment then
anonymous
  • anonymous
the angle was given in degrees so don't use radian form :)
anonymous
  • anonymous
omg 6.76
anonymous
  • anonymous
You are amazing holy christ
anonymous
  • anonymous
i have 3 more answers but with my new found knowledge maybe i can solve them on my own lol
anonymous
  • anonymous
questions not answers*
anonymous
  • 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
  • anonymous
we didn't need to do all that last part....
anonymous
  • anonymous
lol its fine
anonymous
  • anonymous
Do you mind staying for just 3 more questions?
anonymous
  • 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
  • anonymous
Unfortunately, I really have to go. The custodian is starting to wonder why I'm still here :)
anonymous
  • anonymous
lol alright see you then thanks for the help and time once again!
anonymous
  • anonymous
no problem! Best of luck on the rest of your problems :)
anonymous
  • anonymous
lol thank you

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