Question

At the base of ΔABC is the rectangle BCDE, CD = 3 cm, AC = 12 cm, and ∠ACB = 30°. Find the length of AE.

Answer 1

BCDE is a rectangle, AB ⟂ BC and BE = CD = 3 cm.

In right △ABC,

angle at C is 30^∘

AC = 12 cm

AB = AC ⋅ sin 30°

= 12 ⋅ `1/2` = 6 cm

The whole vertical from A down to E is

AE = AB + BE 

= 6 + 3

= 9 cm