SOLUTION: Triangle ABC is isoceles with ABis equal to AC 7.5cm and BC is 9cm. The height AD from A to BC , is 6cm. Find the area of triangle ABC. What will the height be from C to AB i.e CE

Algebra ->  Triangles -> SOLUTION: Triangle ABC is isoceles with ABis equal to AC 7.5cm and BC is 9cm. The height AD from A to BC , is 6cm. Find the area of triangle ABC. What will the height be from C to AB i.e CE       Log On


   

Question 165697: Triangle ABC is isoceles with ABis equal to AC 7.5cm and BC is 9cm. The height AD from A to BC , is 6cm. Find the area of triangle ABC. What will the height be from C to AB i.e CE
Answer by jojo14344(1513) About Me  (Show Source):
You can put this solution on YOUR website!

I'll leave the sketch with you okay, & hopefully we can follow together:
We find first the Area=%281%2F2%29bh
where, BC=base=9cm, & AD=height=6cm
So, A=%281%2F2%29%289%29%286%29
A=27cm%5E2
Now , next is interesting in finding CE?
We first get angle%28B%29 by trigo function of right triangle. How?
Since AD split the base(BC) in to half, side%28BD%29=9%2F2=4.5cm right? Same as side%28DC%29.
That forms a right triangle (ADB).
sin%28beta%29=opp%2Fhyp=AD%2FAB=6%2F7.5=0.80
%28beta%29=sin%5E-1%280.80%29
highlight%28%28beta%29=53.13%5Eo%29
.
Now we know line CE(?) cuts line AB into half:7.5%2F2=3.75cm=BE, right?
That forms a triangle BCE and we'll use Cosine Law in getting line CE.
c%5E2=a%5E2%2Bb%5E2-2abcos%28beta%29
where ---system%28a=BC=9cm%2Cb=BE=3.75cm%2Cc=CE%29
Continuing,
c%5E2=9%5E2%2B3.75%5E2-2%289%29%283.75%29cos%2853.13%29
c%5E2=81%2B14.0625-40.50=95.0625-40.50
c=sqrt%2854.5625%29
highlight%28c=7.38cm=CE%29
Thank you,
Jojo