Question

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 1

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.