Answer
Find out the how far from the wall is the bottom of the ladder.
To prove
As given
A ladder, 500 cm long, leans against a building.
If the angle between the ground and the ladder is 57 degrees .
Now by using the trignometric identity
[tex]cos \theta = \frac{Base}{Hypotenuse}[/tex]
As
[tex]\theta = 57^{\circ}[/tex]
Hypotenuse = 500 cm
put in the above trignometric identity
[tex]cos 57^{\circ} = \frac{Base}{500}[/tex]
Take
cos 57° = 0.54464 (approx)
Base = 0.54464 × 500
Base = 272 .32 cm
Therefore the wall is 272.32cm far from the bottom of the ladder .
The distance from the wall to the base of the ladder is 272.32 cm.
The situation forms a right angle triangle.
Right angle triangle are triangles that have one of it's angles as 90 degrees.
Therefore, the length of the ladder is the hypotenuse of the triangle formed. The distance from the wall to the bottom of the ladder is the adjacent side of the triangle.
Therefore,
cos 57° = adjacent / hypotenuse
cos 57° = a / 500
cross multiply
a = 500 cos 57°
a = 500 × 0.54463903501
a = 272.319517508
a = 272.32 cm
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