1.

a ladder 15m long just reaches the top of a vertical wall if the ladder makes an angle of 60° with the wall find the height of the wall​​

Answer»

em>SOLUTION :-

Length of the LADDER = 15 m

Ladder makes an angle of 60° with the wall.

Let the triangle made be ΔPQR.

Diagram is in the attachment.

Then,

HEIGHT of the wall = PQ

Ground = QR

Ladder = PR = 15M (Given)

∠PQR = 90°

∠QPR = 60° (Given)

By Angle Sum Property,

=> ∠PQR + ∠QRP + ∠QPR = 180°

=> 90° + ∠QRP + 60° = 180°

=> 150° + ∠QRP = 180°

=> ∠QRP = 180° - 150°

=> ∠QRP = 30°

\longrightarrow SIN 30° = \dfrac{PQ}{15\:m}

[sin 30° = \dfrac{1}{2}]

\longrightarrow \dfrac{1}{2}=\dfrac{PQ}{15\:m}

\longrightarrow \dfrac{15\:m}{2}=PQ

\longrightarrow 7.5 m = PQ

Hence, Height of the wall = PQ = 7.5 m.


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