Question

Jasmyn is standing at the point of tangency to a wishing

Answer 1

Answer:

The value of   $x=17 ft$.

Step-by-step explanation:

Diagram of the given scenario shown below.

Given that,

Distance from bench to Jasmyn is   $PA=27ft$.

Distance from bench to Willard is $PB=(2x-7)ft$.

From the Question,

The given wishing well is a circle and all the distance are tangent to the circle.

So, Triangle formed by these points are such as Δ$PAO$ and Δ$PBO$.

Now, taking both Δ$PAO$ and Δ$PBO$.

   ⇒             $AO = BO$                                     {Radius of circle are equal}

   ⇒             $PO=PO$                                     {Common side}

   ⇒          ∠$PAO =$ ∠$PBO$                              {radius is always perpendicular                                                                          

                                                                           to the point of tangent }

∴            Δ$PAO$ ≅ Δ$PBO$                                  {By SAS congruence theorem}

Therefore,   $PA=PB$         ....(1)                             {corresponding part of

                                                                           congruence triangle (CPCT)}

Thus,

   ⇒                $2x-7=27$                                 {from equation (1)}

   ⇒                      $2x=34$    

   ⇒                        $x=17 ft$

Hence, The value of   $x=17 ft$.