Question

In the given figure; ∠C = 90^o and D is mid-point of AC.
Find : 
(i) `(tan∠CAB)/ (tan∠CDB)` (ii) `(tan∠ABC)/ (tan∠DBC)`

Answer 1

Since D is mid-point of AC so AC = 2DC

(i) `(tan∠CAB)/ (tan∠CDB)`

= `("BC"/"AC")/("BC"/"DC")`

= `"BC"/"2 DC"."DC"/"BC"`

= `(1)/(2)`

(ii) `(tan∠ABC)/ (tan∠DBC)`

= `("AC"/"BC")/("DC"/"BC")`

= `"2 DC"/"BC"."BC"/"DC"`

= 2