Question

A ladder 6m long leans against a wall and makes an angle of 50 degrees with the wall.find the distance between the wall and the foot of the ladder,correct to two decimal places.
Hint : cos 50=0.6427

Answer 1

To find the distance between the wall and the foot of the ladder, we can use the cosine function in trigonometry. The cosine of an angle in a right triangle is defined as the length of the adjacent side divided by the length of the hypotenuse.

Given:
- The length of the ladder (the hypotenuse, \( H \)) = 6 meters
- The angle between the ladder and the wall = 50 degrees
- \(\cos(50^\circ) = 0.6427\)

We need to find the distance between the wall and the foot of the ladder (the adjacent side, \( A \)).

Using the cosine formula:
\[
\cos(\theta) = \frac{\text{adjacent}}{\text{hypotenuse}}
\]

Substitute the given values:
\[
0.6427 = \frac{A}{6}
\]

Solving for \( A \):
\[
A = 6 \times 0.6427
\]

Calculating this:
\[
A = 3.8562
\]

Therefore, the distance between the wall and the foot of the ladder is approximately \(3.86\) meters, correct to two decimal places.