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Mathematics

BCDE is a square with side 90 cm and ∠F = 45°. The length of AF is :

  1. 60260\sqrt{2} cm

  2. 90290\sqrt{2} cm

  3. 1202120\sqrt{2} cm

  4. 1802180\sqrt{2} cm

BCDE is a square with side 90 cm and ∠F = 45°. The length of AF is : Heights and Distances, Concise Mathematics Solutions ICSE Class 10.

Heights & Distances

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Answer

Since, BCDE is a square.

∴ BE = CD = 90 cm.

We know that,

tan θ = PerpendicularBase\dfrac{\text{Perpendicular}}{\text{Base}}

From figure,

∠AEB = ∠EFD = 45° (Corresponding angles are equal)

In △ ABE,

⇒ tan 45° = ABBE\dfrac{AB}{BE}

⇒ 1=AB901 = \dfrac{AB}{90}

⇒ AB = 90 cm.

From figure,

AC = AB + BC = 90 + 90 = 180 cm.

We know that,

sin θ = PerpendicularHypotenuse\dfrac{\text{Perpendicular}}{\text{Hypotenuse}}

In △ ACF,

⇒ sin 45° = ACAF\dfrac{AC}{AF}

⇒ 12=180AF\dfrac{1}{\sqrt{2}} = \dfrac{180}{AF}

⇒ AF = 1802180\sqrt{2} cm.

Hence, Option 4 is the correct option.

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