The complete question in the attached figure
we know that
<span>applying the Pythagorean theorem in triangle ABC
</span>AC²=AB²+BC²----------> AB²=AC²-BC²---------> 10²-8²-------> AB²=36-----> AB=6
in the triangle ABC
tan a=BC/AB--------> 8/6--------> tan a=4/3
tan c=AB/BC--------> 6/8--------> tan c=3/4
in the triangle ABD
tan a=BD/AD---------> tan a=BD/x-------> BD=x*tan a
BD=x*(4/3)-----------> equation 1
in the triangle BDC
tan c=BD/DC------------------> BD=(10-x)*tan c------> BD=(10-x)*(3/4)
BD=(10-x)*(3/4)-------------> equation 2
equal 1 and 2
x*(4/3)=(10-x)*(3/4)------> 16x=9*(10-x)--------> 16x=90-9x----> 25x=90
x=90/25-----------> x=3.6
BD=x*(4/3)--------> BD=3.6*(4/3)----------> BD=4.8 units
the answer is BD=4.8 units
we know that
<span>applying the Pythagorean theorem in triangle ABC
</span>AC²=AB²+BC²----------> AB²=AC²-BC²---------> 10²-8²-------> AB²=36-----> AB=6
in the triangle ABC
tan a=BC/AB--------> 8/6--------> tan a=4/3
tan c=AB/BC--------> 6/8--------> tan c=3/4
in the triangle ABD
tan a=BD/AD---------> tan a=BD/x-------> BD=x*tan a
BD=x*(4/3)-----------> equation 1
in the triangle BDC
tan c=BD/DC------------------> BD=(10-x)*tan c------> BD=(10-x)*(3/4)
BD=(10-x)*(3/4)-------------> equation 2
equal 1 and 2
x*(4/3)=(10-x)*(3/4)------> 16x=9*(10-x)--------> 16x=90-9x----> 25x=90
x=90/25-----------> x=3.6
BD=x*(4/3)--------> BD=3.6*(4/3)----------> BD=4.8 units
the answer is BD=4.8 units
