Question

What is the geometric mean of the measures of the segments AD and DC? Show your work.

Answer 1

Mean = 7.525 In

Explanation:

Let BD =X

let dab = a

Let dcb = b

X/sin a= 12

X/sinb= 5

a+b = 90

b= 90-a

X/sinb = x/sin(90-a)= 5

Equating the value of x

12sina = 5sin(90-a)

12sina= 5sin90 - 5sina

Recall that Sin 90= 1

12sina= 5 -5sina

17sina= 5

Sina= 5/17

a= sin^-15/17

a= sin^-1 *0.2941

a= 17.1°

a+b=90

b = 90-a

b = 90-17.1

b =72.9°

X/Sina= 12

X/sin17.1= 12

X = 12*0.2940

X= 3.528

X= 3.5 In

12²-3.5²= AD²

5²-3.5²= DC²

144-12.25= AD²

25-12.25= DC²

131.75= AD²

12.75= DC²

AD= 11.48 In

DC= 3.57 In

Mean =( 11.48+3.57)/2

Mean = 15.05/2

Mean = 7.525 In