Question

answer plz .........​

Answer 1

Given :-----

• Angle NCD = 30°
• angle BAM = 45°
• DN is perpendicular to BC.
• AM is perpendicular to BC.
• AB = √10
• BM = AM = AD
• AD is parallel to BC.

To Find :----

• Length of BC ?

Formula used :----

• Pythagoras theoram .
• Tan30° = 1/√3
• Tan@ = Perpendicular/Base

Solution :------

First lets take Right ∆ AMB ,

since AM = BM ,

so, angle BAM = angle ABM = 45° ( Equal sides opposite angles are Equal ) .

Now , let AM = BM = x metre .

than , by pythagoras theoram we get,

→ AM² + BM² = AB²

putting values we get,

→ x² + x² = (10√2)²

→ 2x² = 200

→ x² = 100

→ x = 10m = AM = BM .

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Now, since , AD is also equal to AM and BM , AD is also Equal to 10m .

Now, AD is parallel to MN, and AM is parallel to DN,

Hence,

→ AD = MN = 10m

→ AM = DN = 10m

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Now, in Right ∆DNC , we have ,

→ DN = 10m

→ angle DCN = 30°

above told Trignometric formula ,

→ Tan30° = DN/NC

→ 1/√3 = 10/NC

→ NC = 10√3 m

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So, Length of BC

= BM + MN + NC

= 10 + 10 + 10√3

= 20 + 10√3

= 10(2+√3) m

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Hence, length of BC will be 10(2+√3) m

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