Question

11. How many kilometers is it from the main gate to Manatee Springs? (Hint: To convert from

yards to kilometers, multiply by 0.0009144). Round answer to the nearest hundredth kilometer.

Manatee Springs

Elephant

House

3,500 yds

4,200 yds

Train Depot

2,000 yds

Bird Sanctuary

Main Gate

(SHOW WORK)

Answer 1

6 km

Explanation:

Let us assume the following items

the Point at Train depot = T

The Point at Main gate = M

The Point at Bird sanctuary = B

The Point at Elephant house = E

The Point at manatee Springs = S

As we can see that there are two triangles namely TMB and TSE.

Mentioned that

MTB = ∠STE

∠TMB = ∠TSE

∠TBM = ∠TES.

According to the Angle-angle-angle (AAA similarity)

So, the triangles TMB and TSE are the same.

`(TM)/(TS) = (TB)/(TE) \\\\ (TM)/(4,200) = (2,000)/(3,500)`

So, the TM is 2400 yds

Now the Distance between Main gate M and manatee Spring S is

MS = MT + TS

= 2,400 + 4200

= 6600 yds

Now the MS is

= 6600 × 0.0009144 km

= 6.035 km

≅ 6 km