A 12-foot ladder is placed 4 feet away from a house as shown. A 12 foot ladder is leaning against a house to form angle x. The distance between the house and the bottom of the ladder is 4 feet. The angle between the house and the ground is 90 degrees.

What is the value of x, rounded to the nearest degree?

x ≈
°

According to the manufacturer, if the angle the ladder forms with the ground, x, is between 70° and 75°, then it meets safety standards.

Is this ladder being used safely?

#1.

cos(x) = adjacent/hypotenuse = 4/12 ≈ 0.3333  ⇒ x ≈ 71°

#2

71° is  between 70° and 75°, so the answer is yes, the ladder being used safely.

Step-by-step explanation:

given that triangle abc is transformed two times to get triangle

a"b"c"

first abc is transformed in to a'b'c' as follows:

the coordinates of a are (1,-1) and transformed into a'(-1,1)

similarly b (4,-2) became b'(-4,2) and

c(7,-2) became c'(-7,2)

i.e. (x,y) becomes (-x,-y)

this is nothing but reflection about a point here origin.

thus first transformation is reflection on the origin.

next is exactly shifting 3 units down

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