A ladder is placed against a wall such that it reaches the top of the wall at a height of 6 meters. The ladder is inclined at an angle of 60 degrees from the ground. How far is the ladder from the foot of the wall?
(Please show work)

the distance between foot of the ladder and the wall is 3.464 m.

Step-by-step explanation:

Here AB represents height of the wall, BC represents the distance between the wall and the foot of the ladder and AC represents the length of the ladder.

In the right triangle ABC, the side which is opposite to angle 60 degree is known as opposite side (AB), the side which is opposite to 90 degree is called hypotenuse side (AC) and remaining side is called adjacent side (BC)

Now, we need to find the distance between foot of the ladder and the wall. That is, we have to find the length of BC.

tan θ  =  Opposite side/Adjacent side

tan60°  =  AB/BC

√3  =  6/BC

BC  =  6/√3

BC  =  (6/√3) x (√3/√3)

BC  =  (6√3)/3

BC  =  2√3

Approximate value of √3 is 1.732

BC  =  2 (1.732)

BC  =  3.464 m

So, the distance between foot of the ladder and the wall is 3.464 m.

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step-by-step explanation:

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