SOLUTION: In triangleABC measure of angle A=30 degrees and measure of angle C=90 degrees. If the length of BC is four more than one-fourth of AB, find the length of the longer leg of the tri

Algebra ->  Triangles -> SOLUTION: In triangleABC measure of angle A=30 degrees and measure of angle C=90 degrees. If the length of BC is four more than one-fourth of AB, find the length of the longer leg of the tri      Log On


   

Question 191742: In triangleABC measure of angle A=30 degrees and measure of angle C=90 degrees. If the length of BC is four more than one-fourth of AB, find the length of the longer leg of the triangle.
Answer by RAY100(1637) About Me  (Show Source):
You can put this solution on YOUR website!
draw triangle abc
a=30deg, c=90 deg, therefore b=60 deg (sum of angles = 180)
bc = .25 ab +4 (given)
but in 30-60-90 triangle, bc = 1/2 ab
therefore ab = 1/2 ab +8
simplifying 1/2 ab = 8
ab=16
subst bc = .25 (16) +4 = 8
using pythagorous
16^2 - 8^2 = 256 - 64 = 192 = ac^2
ac = (64 *3)^.5 = 8 *3^.5 or 8 sq rt 3
check 30-60-90 triangle makes 1-2-sq rt 3 sides, 8-16-8sqrt3 ok