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