Question

in the figure given below, D is the midpoint of AC of triangle ABC where angle C = 90°. If tan A = 3/4, then (tan angle ABC) / (tan angle DBC) = ____​

Answer 1

Answer:

2

In the given figure,

∠C=90∘

In △ABC,

tan∠ABC=BP=BCAC

In △CDB,

tan∠DBC=BP=BCCD

Now,

tan∠DBCtan∠ABC=BCCDBCAC

tan∠DBCtan∠ABC=CDAC

tan∠DBCtan∠ABC=CD2CD

tan∠DBCtan∠ABC=2 (D is mid point of AC)