sisxixon said:
In triangle ABC, D is on AC such that angle ABC= angle ADB . If AD=2 cm, DC=1cm, and BC=4cm, what is the length of AB , in centimeters?
I'm so lost. I started by drawing the figure, but messed that up quite awfully, too. Can someone help?
OK; draw triangle ABC making angle at C = 38 degrees;
use inches: make BC=4 inches and AC = 3 inches;
now make point D on AC 1 inch from C: so DC = 1 inch and AD = 2 inches;
use ACTUAL inches and make angle C ACTUALLY 38 degrees:
then you'll be able to "see" what's going on!
Now join BD. You'll "see" that angle ABC is equal to angle ADB.
Now, triangle ABC and triangle ABD both have angle BAC: see that?
So, since angle ABC = angle ADB, these triangles are similar: ok?
Let x = AB and y = BD.
Since triangles are similar, then:
x / y = 3 / 4 [1] : that's sideAB / sideBD = sideAC / sideBC
and
x / 4 = y / 2 [2] : that's sideAB / sideBC = side BD / sideAD
[1]: y = 4x / 3
[2]: y = 8 / x
so:
4x / 3 = 8 / x
4x^2 = 24
x^2 = 6
x = sqrt(6) = AB
If you need length of BD, then, from [2]: y = 8 / sqrt(6)
The angles are approx: A = 93.9, B = 48.4, C = 37.7 (that's why I told you to use 38!)
