Question

In the given figure, AB and EC are parallel to each other. Sides AD and BC are 1.5 cm each and are perpendicular to AB. Given that ∠AED = 45° and ∠ACD = 30°. Find:
a. AB
b. AC
c. AE

Answer 1

a. In right ΔADC,

tan30° = `"AD"/"DC"`

⇒ `(1)/sqrt(3) = (1.5)/"DC"`
⇒ DC = `1.5sqrt(3)`
Since AB || DC and AD ⊥ EC, ABCD is a parallelogram and hence opposite sides are equal.
⇒ AB
= DC
= `1.5sqrt(3)"cm"`.
b. In right ΔADC,

sin30° = `"AD"/"AC"`

⇒ `(1)/(2) = (1.5)/"AC"`
⇒ AC
= 2 x 1.5
= 3cm.
c. In right ΔADE,

sin45° = `"AD"/"AE"`

⇒ `(1)/sqrt(2) = (1.5)/"AE"`
⇒ AE = `1.5sqrt(2)`.