Question

A ladder 9.00m long leans against the side of a building .If the ladder is inclined at an angle of 75.0 to the horizontal,what is the horizontal distance from the bottom of the ladder to the building?

Answer 1

A ladder 9.00m long leans against the side of a building. If the ladder is inclined at an angle of 75.0 to the horizontal, what is the horizontal distance from the bottom of the ladder to the building?

**Solution:**

$\alpha = 75{}^{\circ}$ – the angle at which the ladder is inclined to the horizontal;

$L = 9.00\mathrm{m}$ – length of the ladder;

$d$ – horizontal distance from the bottom of the ladder to the building.

Cosine of the angle alpha from the right triangle ABC:

$$\cos \alpha = \frac {B C}{A B} = \frac {d}{L}$$ $$d = L \cdot \cos \alpha = 9.00 \, \mathrm{m} \cdot \cos 75{}^{\circ} = 2.33 \, \mathrm{m}$$

**Answer:** horizontal distance from the bottom of the ladder to the building is 2.33m