Question

In the given figure; ∠C = 90⁰ and D is Midpoint of AC. Find :
$(i) \: \dfrac{tan ∠CAB }{tan ∠CDB } \\ \\ (ii) \frac{tan∠ABC }{tan∠DBC }$
​

Answer 1

Step-by-step explanation:

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)

have a wonderful day ahead

Answer 2

In the given figure; ∠C=90

and D is midpoint of AC. Find

tan∠DBC

tan∠ABC

In the given figure,

∠C=90

In △ABC,

tan∠ABC=

B

P

=

BC

AC

In △CDB,

tan∠DBC=

B

P

=

BC

CD

Now,

tan∠DBC

tan∠ABC

=

BC

CD

BC

AC

tan∠DBC

tan∠ABC

=

CD

AC

tan∠DBC

tan∠ABC

=

CD

2CD

tan∠DBC

tan∠ABC

=2 (D is mid point of AC)