Question

In rectangle ABCD, DB = 10 cm and BC = 5 cm. Find ∠BDC and the length of AB.

Answer 1

Given:

□ABCD

Diagonal DB = 10 cm

Side BC = 5 cm

In right △DBC (right angle at C):

DC = `sqrt(DB^2 − BC^2)`

DC = `sqrt(10^2 − 5^2)`

DC = `sqrt(100 − 25)`

DC = `sqrt75`

DC = `5sqrt3` cm

Since DC = ABDC = ABDC=AB (opposite sides of a rectangle),

AB = DC = `5sqrt3`

tan ∠BDC (at D)

tan ∠ BDC = `(BC)/(DC) = 5/(5sqrt3) = 1/sqrt3`

= ∠BDC = 30°