In right triangle ABC, we have \(\angle BAC = 90^\circ\)and D is the midpoint of \(\overline{AC}.\)If AB=7 and BC=25, then what is \(\tan \angle BDC\)?
+776 Is there a diagram? (my bad, i didnt know that a diagram was not needed, aka my trig skills = not that great)
+130081 B
7 25
A D 12 C
AC = sqrt ( 25^2 - 7^2] = sqrt ( 625 - 49) = sqrt (576) = 24
And since D is the midpoint of AC, then DC = (1/2)24 = 12 = AD
And tan BDA = 7/12
And angle BDC is supplemental to angle BDA
So.....BDC = 180° - BDA
So.....letting BDA = theta and using a trig identity we have
tan ( 180° - theta) = tan (BDC) = - tan (theta) = - tan(BDA) = -7/12
