A landscaping company was hired to build pathways to a duckpond. One pathway needs to be tangent to the pond, and the other will become a bridge that crosses over the water. Use the diagram below to answer Part A and Part B.

The question is incomplete! Complete question along with answer and step by step explanation is provided below.

Question:

A landscaping company was hired to build pathways to a duckpond. One pathway needs to be tangent to the pond, and the other will become a bridge that crosses over the water. Use the diagram below to answer Part A and Part B.

Part A: Determine the length of the bridge. Use mathematics to explain how you arrived at your answer.

Part B: The contractor is charging $1500 a foot to construct the bridge, if your budged for the bridge is $150000, will you have enough money to pay for the bridge?

Part A: The length of the bridge is 80 feet.

Part B: The budget for the construction of bridge ($150,000) is less than the cost of constructing bridge ($120,000) therefore, we have enough money to pay for the bridge.

Step-by-step explanation:

Part A:

Refer to the attached diagram, here cd is the tangent segment and and ac is the secant.

From the properties of tangent of a circle, we have the following relation,

ac/cd = cd/bc

ac*bc = cd²   eq. 1

Let x is the length of the bridge that we want to find out.

ab = x

and

bc = 10 feet

ac = ab + bc

ac = x + 10

cd = 30 feet

so the eq. 1 becomes

ac*bc = cd²

(x + 10)(10) = 30²

10x + 100 = 30²

10x + 100 = 900

10x = 900 - 100

10x = 800

x = 800/10

x = 80 feet

Therefore, the length of the bridge is 80 feet.

Part B:

Cost per foot = $1500

Length of the bridge = 80 feet

Total cost of constructing bridge = $1500*80

Total cost of constructing bridge = $120,000

The budget for the construction of bridge ($150,000) is less than the cost of constructing bridge ($120,000) therefore, we have enough money to pay for the bridge.

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