In the right △abc, cd is the altitude to the hypotenuse ab and m∠abc=30°. find ad, if bd=54 cm.

The ratios of sides in a 30°-60°-90° triangle are such that the hypotenuse (AB) is double the length of the shortest side (AC). In your triangle, AC is the hypotenuse of similar triangle ACD, which has AD as its shortest side.

Then

(1/2)×(AD+54) = AC

(1/2)×AC = AD

Together, these tell you

AD = (1/4)(AD +54)

3×AD = 54

AD = 18

last option

step-by-step explanation:

given that δdef is right and isoceles,

assuming that side df is the hypotenuse means that de an ef are the other 2 sides that intersect at 90° and are of equal length.

because they are of equal length, we can say that they are congruent

because they intersect at 90°, their slopes must be opposite reciprocals.

only the last option satisfies these conditions.

.95

step-by-step explanation: