Which is the best approximation for the measure of angle abc? a) 27.7° b) 31.7° c) 58.3° d) 62.3°

answer: the best approximation for the measure of angle abc applying the trigonometric function cosine in the right triangle abc is

option c) 58.3°

solution:

hypotenuse: ab=20 cm largest side opposite to the right angle (angle of 90°)

angle abc = x =?

adjacent leg to angle abc = bc = 10.5 cm

we have the adjacent side to the angle x and the hypotenuse of the triangle, and we need the angle. the trigonometric function that relates the adjacent side of an angle with the hypotenuse in a right triangle is cosine:

cos x = adjacent leg / hypotenuse

cos x = bc / ab

replacing the given values:

cos x = (10.5 cm) / (20 cm)

cos x =   0.525

solving for x:

x= cos^(-1) (0.525)

x=58.33175674°

rounding to one decimal place:

x=58.3°

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)

step-by-step explanation:

a and d