Jasmyn is standing at the point of tangency to a wishing
well, 27 feet from a bench. Her friend Willard is at the other
point of tangency. Determine the value of x.
w
(2x - 7) ft
27 ft
Sac

The value of   .

Step-by-step explanation:

Diagram of the given scenario shown below.

Given that,

Distance from bench to Jasmyn is   .

Distance from bench to Willard is .

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 and Δ.

Now, taking both Δ and Δ.

   ⇒                                                 {Radius of circle are equal}

   ⇒                                                 {Common side}

   ⇒          ∠ ∠                              {radius is always perpendicular                                                                          

                                                                           to the point of tangent }

∴            Δ ≅ Δ                                  {By SAS congruence theorem}

Therefore,           ....(1)                             {corresponding part of

                                                                           congruence triangle (CPCT)}

Thus,

   ⇒                                                 {from equation (1)}

   ⇒                          

   ⇒                        

Hence, The value of   .

c.   x=2.4cm

step-by-step explanation:

similar triangles are triangles which have the same shape but not the same size. this means their angle measures are equal but their side lengths are not instead they are proportional. to solve, we will set up a proportion and solve.

a proportion is two equal ratios set equal to each other. we form the ratios by finding corresponding sides (sides which match to each other on both triangles by their position). out ratios will be one side of the small triangle over the corresponding side on the big triangle as shown below:

.

to solve the proportion, we'll cross multiply by multiplying numerator with denominator across the equal sign.