Question

If a ladder is making an angle of elevation 60 degree with the wall and the distance between the foot of the ladder and wall is 2.5m,how long the ladder will be:-

Answer 1

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?

If the angle of elevation is 60 degrees, then we have a 30–60–90 right triangle (assuming the wall is vertical and the ground is horizontal), with the shortest side being 4.6 m in length.

In such a triangle, the hypotenuse is twice the length of the shortest side.

Answer 2

Answer:

The length of the ladder is 5 m

Step By Step Solution:

Angle of elevation of the ladder = 60°

Distance between the foot of the ladder and the wall = 2.5 m

Firstly, we represent the given data in the form of a diagram (Refer to the diagram attached)

In the ΔABC, AC is the length of the ladder and BC is the distance between the foot of the ladder and the wall. As it is a right-angles triangle,

$\Rightarrow \cos 60^\circ = \frac{{{\text{adjacent side}}}}{{{\text{hypotenuse}}}}$

$\Rightarrow \cos 60^\circ = \frac{{{\text{BC}}}}{{{\text{AC}}}} \hfill$

$\Rightarrow \frac{1}{2} = \frac{{2.5}}{{{\text{AC}}}}$

$\Rightarrow {\text{AC = 2}}{\text{.5}} \times {\text{2}}$

$\Rightarrow {\text{AC = 5 m}}$

$\boxed{{\text{The length of the ladder is 5 m}}}$