Question

A ladder 17 m long reaches a window on a wall, which is 8 m above the ground, on
one side of the street. Find the distance of the foot of the ladder from the wall.​

Answer 1

Given :-

Height of the ladder = 17 m

Height of the window = 8 m

To Find :-

The distance of the foot of the ladder from the wall.

Solution :-

The given set-up forms a triangle

Let the unknown side be x

Using Pythagoras theorem,

17² = 8² + x²

=> 289 - 64 = x²

=> x² = 225

$\implies\: x\: =\: {\sqrt{225}}$

=> x = 15

Required answer = 15 m

Answer 2

✬ Distance = 15 m ✬

Step-by-step explanation:

Given:

• Length of ladder is 17 m.
• Length of window is 8 m.

To Find:

• What is the distance of the foot of ladder from wall ?

Solution: Let PQ be the window and PR be a ladder and QR be the distance between foot of ladder and window.

Here in right angled triangle PQR we have

• PQ = 8 m {perpendicular}

• PR = 17 m {hypotenuse}

• QR = {base}

• ∠PQR = 90°

Using Pythagoras theorem in ∆PQR

★ H² = Perpendicular² + Base² ★

$\implies{\rm }$ PR² = PQ² + QR²

$\implies{\rm }$ 17² = 8² + QR²

$\implies{\rm }$ 289 – 64 = QR²

$\implies{\rm }$ √289 – 64 = QR

$\implies{\rm }$ √225 = QR

$\implies{\rm }$ 15 = QR

Hence, the distance between the foot of ladder from the wall is 15 m.