Question

The following sides of triangle upper C upper B upper A are labeled: upper A upper C is lower b, upper C upper B is lower a, and upper A upper B is lower c. Upper A upper D is labeled lower m, and upper D upper B is labeled lower n. Right angle symbols are drawn at angle upper A upper C upper B and angle upper C upper D upper B.

Given that n=48
𝑛
=
48
and a=60
𝑎
=
60
, what is the value of b?

(1 point)
Responses

b=45
𝑏
=
45
b is equal to 45

b=27
𝑏
=
27
b is equal to 27

b=75
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 = c·n and b^2 = c·m, with c = m + n. Here 60^2 = c·48 → c = 3600/48 = 75. Then m = 75 − 48 = 27, so b^2 = 75·27 = 2025 → b = 45.