Question

Part A is asking how long the bridge is and Part B is asking how expensive it would be if each foot it 1500

Answer 1

(a)80 feet

(b)$120,000

Explanation:

Part A

Intersecting Secant-Tangent Theorem

If a tangent segment and a secant segment are drawn to a circle from an exterior point, then the square of the measure of the tangent segment is equal to the product of the measures of the secant segment and its external secant segment.

In the attached diagram, the theorem applied is:

`|AX|^2=|UX|*|TX|`

Comparing with our diagram:

|AX|=30 feet

|UX|=10 feet

Length of the Bridge,L

Therefore:

`30^2=10 X ($Length of the Bridge+10)`

900=10(L+10)

L+10=900/10

L+10=90

L=90-10=80 feet

Length of the Bridge=80 feet

Part B

If each foot costs $1500

Cost of the bridge=$1500*80=$120,000