D is on side AB of Triangle ABC. We know triangle ABC\(\sim\)triangle ACD and angle A=48. If BC=BD, what is angle B in degrees?

here is the image:

https://docs.google.com/document/d/1f9ygPhFBH44Ko1mmiGzzfVsAWfiOA3pX50IsnYQ9OBM/edit?usp=sharing

I'll add the pic - Melody

CCeed Oct 8, 2021

#1**+2 **

I get 28 degrees. (which I have not checked)

Let's see what catmg comes up with.

Melody Oct 9, 2021

#3**+2 **

Nice. :))

I really miss going on this forum more often.

Sadly, school is quite busy.

=^._.^=

catmg
Oct 9, 2021

#5**+1 **

You are the one who did the nice work Catmg.

Yes school is busy, so is life for younger people.

Most of the people who are here a lot, to answer questions I mean, are retired.

It can continue to be a nice hobby for you though :))

Melody
Oct 9, 2021

#2**+2 **

Hello CCeed :))

Let angle B = x

angle A = 48

angle C = 132 - x

Since ABC ~ ACD

angle B = angle ACD = x

angle C = angle CDA = 132 - x

Since BC = BD

BCD = BDC

BCD + BDC + B = 180 degrees

BDC + BDC + x = 180 degrees

BDC = (180-x)/2

CDA + CDB = 180

132 - x + (180-x)/2 = 180

x = 28

I hope this helped. :))

=^._.^=

catmg Oct 9, 2021

#4**+1 **

I find it quite difficult to get my head around geometry questions such as this.

So I will give you some insight as to how I go about it.

I drew the diagram and shade the smaller one.

then I said the smallest side of the big triangle is AC which corresponds to the smallest side of the small diagram AD

then I said the biggest side of the big triangle is AB which corresponds to the biggest side of the small diagram AC

Now I draw the corresponding triangles like this:

And then I take it from there.

I suppose it is too slow long term but while you are getting the hang of it it can help.

Melody Oct 9, 2021