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
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


Use the image to answer the question.

A line, x, divides a right triangle from the vertex opposite the hypotenuse to the hypotenuse. The line x forms a second right angle, marked by a small square, where it meets the hypotenuse, and it divides the hypotenuse into 6 and 3.

Use the geometric mean to find x. Round your answer to the nearest tenth.

(1 point)
x=

Answer 1

First problem: b = 45.
Reason: a^2 = c·n ⇒ 60^2 = c·48 ⇒ c = 75. Then b^2 = c^2 − a^2 = 75^2 − 60^2 = 2025 ⇒ b = 45.

Second problem: x = sqrt(6·3) = sqrt(18) ≈ 4.2.