In the right △ABC, CD is the altitude to the hypotenuse AB and m∠ABC=30°. Find AD, if BD=54 cm. Answer:

Question

Mathematics

Ariel Riley

24 July, 21:31

In the right △ABC, CD is the altitude to the hypotenuse AB and m∠ABC=30°. Find AD, if BD=54 cm. Answer:

+5

Answers (1)

Know the Answer?

Maya Gardner · Answer 1

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