Question

The angle of elevation of a ladder leaning against a wall is 60 degrees and the foot of the ladder is 4.6 m away from the wall. The length of the ladder is ___ m. Type your answer below!

Answer 1

Angle = 60º and distance between wall and ladder= 4.6 m.

Length of ladder= 2 x distance between wall and ladder

= (2 x 4.6) m

= 9.2 m

Answer 2

Given :

Angle of elevation = 60°

Distance of the foot from the wall = 4.6 m

To Find :

The length of the ladder.

Solution :

Ladder leaning against the wall forms a right-angled triangle where, base of the triangle gives the distance between foot of the ladder and wall, Hypotenuse of the triangle gives the length of the ladder. Perpendicular represents the length of the wall.

In right-angled triangle ABC,

⇒ cos∅             = $\frac{Base}{Hypotenuse}$

⇒ cos60           =  $\frac{4.6}{Hypotenuse}$

⇒    $\frac{1}{2}$                 =  $\frac{4.6}{Hypotenuse}$

∴ Hypotenuse  =  9.2 m

Therefore, the length of the ladder is 9.2 m.