Question

A ladder 7.85 m long leans against the side of a building. If the ladder is inclined at an angle of 66.5° to the horizontal, what is the horizontal distance from the bottom of the ladder to the building?

Answer 1

Answer on Question 61932, Physics, Mechanics, Relativity

Question:

A ladder $7.85 \, m$ long leans against the side of a building. If the ladder is inclined at an angle of $66.5{}^{\circ}$ to the horizontal, what is the horizontal distance from the bottom of the ladder to the building?

Solution:

Here's the sketch of our problem:

Let $l = 7.85 \, m$ is the length of the ladder, $\theta = 66.5{}^\circ$ is the angle at which the ladder inclined to the horizontal and $d$ is the horizontal distance from the bottom of the ladder to the building. Then, we can find $d$ from the right triangle $OAB$ :

$$\cos \theta = \frac {O A}{O B} = \frac {d}{l}.$$

From this formula we can find the horizontal distance from the bottom of the ladder to the building:

$$d = l \cdot \cos \theta = 7. 8 5 m \cdot \cos 6 6. 5 {}^ {\circ} = 3. 1 3 m.$$

Answer:

$$d = 3. 1 3 m.$$

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