SOLUTION: in an equilateral triangle ABC with side lengths of 9 inches .ADis an altitude. what is the length of AD?

Algebra ->  Triangles -> SOLUTION: in an equilateral triangle ABC with side lengths of 9 inches .ADis an altitude. what is the length of AD?      Log On


   

Question 953320: in an equilateral triangle ABC with side lengths of 9 inches .ADis an altitude. what is the length of AD?
Found 2 solutions by macston, MathLover1:
Answer by macston(5194) About Me  (Show Source):
You can put this solution on YOUR website!
h=altitude; a=side
h=%281%2F2%29sqrt%283%29a=%281%2F2%29sqrt%283%29%289in%29=0.8660%289in%29=7.79 in
ANSWER: The length of the altitude is 7.79 inches.

Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!

side lengths of s=9in
AD is an altitude
The height divides it into two right triangles, each with a hypotenuse equal to one side (s), a base which is %281%2F2%29s, and then AD the altitude
s%5E2+=+%28s%2F2%29%5E2+%2B+%28AD%29%5E2+
%289in%29%5E2+=+%289in%2F2%29%5E2+%2B+%28AD%29%5E2+
81in%5E2+=+81in%5E2%2F4+%2B+%28AD%29%5E2+
81in%5E2+-81in%5E2%2F4=+%28AD%29%5E2+
81in%5E2+-20.25in%5E2=+%28AD%29%5E2+
60.75in%5E2=+%28AD%29%5E2+
AD=sqrt%2860.75in%5E2%29+
AD=7.794228634059948in+
AD=7.8in+