Problema Solution
In right triangle ABD below, AC is perpendicular to the hypotenuse BD. If the length of AD is 6 units and that of AB is 8 units,then how many units long is AC?
Answer provided by our tutors
draw the right triangle ABD with the right angle at A, legs: AB and AD and hypotenuse BD
then AC is the height towards the hypotenuse BD
AD = 6
AB = 8
using the Pythagorean Theorem we find
BD = (AB^2 + AD^2)^0.5
BD = (8^2 + 6^2)^0.5
BD = 10
the are of this right triangle is A = (AB*AD)/2 as well as A = (AC*BD)/2 thus we have
(AB*AD)/2 = (AC*BD)/2 multiply both sides by 2
AB*AD = AC*BD
AC = (AB*AD)/BD
AC = 8*6/10
AC = 4.8 units
AC is 4.8 units long.