Question

ABCD is a rectangle with AD=12 cm and DC= 20 cm. The line segment DE is drawn making an angle 30° with AD interesting AB in E find the length of DE and AE

Answer 1

cos30°=1/2
In ΔDAE
cos theta= perpendicular/hypotenuse
       cos30 = AD/DE
         √3/2  =12/DE
             DE=8√3
        

Answer 2

Answer:

Step-by-step explanation:Answer :

Given

AD = 12 cm

DC = 20 cm

SO,

AD = BC = 12 cm ( As we know opposite sides of rectangle are equal in length )

DC = AB = 20 cm ( As we know opposite sides of rectangle are equal in length )

And

From given information we form our figure , As :

Now In ∆ DAE , we know

tan 30° = OppositeAdjacent = AEAD

So,

13√ = AE12 ( As we know tan 30° = 13√ )

SO,

AE = 123√ , Now we multiply and divide by 3√ ,And get

AE = 123√×3√3√ = 123√3 = 43√ cm

And

AB = AE + BE

So,

BE = 20 - 43√

And

Cos 30° = AdjacentHypotenuse = ADDE

So,

3√2 = 12DE , So ( As we know Cos 30° = 3√2 )

DE = 243√ , Now we multiply and divide by 3√ ,And get

DE = 243√×3√3√ = 243√3 = 83√ cm

SO,

DE = 83√ cm

And

BE = 20 - 43√ cm ( Ans )

Or

DE = 8 × 1.732 = 13.856 cm

And

BE = 20 - 4 × 1.732 = 20 - 6.928 = 13.072 cm ( As we know 3√ = 1.732 )