A20-foot ladder touches a building 16 feet up the wall. what is the measure of the angle the ladder makes with the ground (macb)?

Choice A) 53 degrees

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Check out the attached image. Notice how I'm only focusing on the triangle. I have erased any other extra lines or unneeded info. We have the opposite side 16 and the hypotenuse 20. We'll use the sine ratio and the arcsine function as well. On your calculator, the arcsine function is "arcsin" or it might be labeled "sin^(-1)"

Let x = measure of angle ACB

sine = opposite/hypotenuse

sin(angle ACB) = (height)/(length of ladder)

sin(x) = 16/20

sin(x) = 4/5

sin(x) = 0.8

x = arcsin(0.8)

x = 53.130102354156

x = 53 when rounded to the nearest whole number

So that's why angle ACB is roughly 53 degrees

δabc ≅ δdcb by sas because

db ≅ ac . . given (side)

bc ≅ bc . . reflexive property (side)

∠dbc ≅ ∠ acb . . alternate interior angles where transversal bc crosses parallel lines bd and ac (included angle)