Aladder is leaning against a wall. the top of the ladder is 4 feet above the ground
and the bottom of the ladder makes an angle of 60° with the ground. how long is the
ladder, and how far from the wall is the bottom of the ladder?

Step-by-step explanation:

The ladder forms a triangle with the wall and ground.

The side of the triangle opposite of the 60° angle is 4 feet.

To find the length of the ladder (the hypotenuse), use sine.

sine = opposite / hypotenuse

sin 60° = 4 / L

L = 4 / sin 60°

L = 4 / (√3 / 2)

L = 8 / √3

L = 8√3 / 3

L ≈ 4.619 feet

To find the distance from the wall, use tangent.

tangent = opposite / adjacent

tan 60° = 4 / x

x = 4 / tan 60°

x = 4 / √3

x = 4√3 / 3

x ≈ 2.309 feet

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step-by-step explanation: