SOLUTION: The Question reads: The folling figures are pairs of similar triangles with some dimensions given. Find the measure of the indicated sides. (2 triangles, one is inside the ot

Algebra ->  Triangles -> SOLUTION: The Question reads: The folling figures are pairs of similar triangles with some dimensions given. Find the measure of the indicated sides. (2 triangles, one is inside the ot      Log On


   

Question 169639: The Question reads:
The folling figures are pairs of similar triangles with some dimensions given. Find the measure of the indicated sides.
(2 triangles, one is inside the other)
Bigger triangle is ACD
Smaller triangle is ABE (inside of ACD)
Angle ACD equal to 90 degrees
Angle ABE equal to 90 degrees
Segment AB is equal to 6
Segment AE is equal to 10
Segment CD is equal to 14
Find segment AC, BE, and AD
Answer by jojo14344(1513) About Me  (Show Source):
You can put this solution on YOUR website!
Let's draw the pairs of Triangles to have a clearer view:

.
We get 1st Angle ALPHA, which will be very helpful:
By Trigo Function: Cos%28alpha%29=adj%2Fhyp=AB%2FAE
alpha=cos%5E-1%28AB%2FAE%29=cos%5E-1%286%2F10%29
alpha=53.13%5Eo
.
We solve for BE?, by Pyth.Teorem:
AE%5E2=AB%5E2%2BBE%5E2
BE%5E2=AE%5E2-AB%5E2=10%5E2-6%5E2=100-36=64
BE=sqrt%2864%29 ---------->highlight%28BE=8%29
We solve for AC?, by Trigo function:
tan%28alpha%29=opp%2Fadj=DC%2FAC
AC=DC%2Ftan%28alpha%29=14%2Ftan53.13%5Eo
highlight%28AC=10.50%29
We solve for AD?, by Trigo function:
sin%28alpha%29=opp%2Fhyp=DC%2FAD
AD=DC%2Fsin%28alpha%29=14%2Fsin53.13%5E0
highlight%28AD=17.50%29
See the 2 pairs of Triangle:

.
thank you,
Jojo