Question

Use the image to answer the question.

On right triangle upper C upper B upper A, the altitude of vertex upper C is drawn as a solid line that extends from upper C to the hypotenuse, upper A upper B. The intersection of the altitude and upper A upper B is labeled upper D.
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Given that n=48
and a=60
, what is the value of b?

(1 point)
Responses

b=45
b is equal to 45

b=27
b is equal to 27

b=75
b is equal to 75

b=36

Answer 1

b = 45

Reason: In a right triangle with altitude to the hypotenuse, a^2 = AB·AD. So AB = a^2/n = 3600/48 = 75. Then b^2 = AB·BD = AB(AB − AD) = 75(75 − 48) = 75·27 = 2025, hence b = √2025 = 45.