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a ladder is leaned against a wall. the distance from the base of the ladder to the wall is 12m.If the ladder is 20m.what angle is it leaning at?

 May 3, 2021
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The ladder makes a right triangle (since we assume the wall makes a right angle with the ground). Thus the wall and ground are our legs and the ladder is our hypotenuse; try to identify that any time you get these word problems where they're building shapes with objects.

 

So if we have a triangle with hypotenuse 20 (length of ladder, and a leg of 12 m, what's the angle? We need a trug function... Is that leg opposite or adjacent to the angle? Well the angle is between the ladder and the ground, so it must be adjacent.

 

What trig function uses the ratio of hypotenuse and adjacent legs? Cosine. So if cos(x) = opp/hy = 12/20 = .6, then all we need is to solve:

 

X = cos^-1(.6)

(The inverse cosine of .6)

 May 3, 2021

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