Given: δabc is a right triangle. prove: a2 + b2 = c2 right triangle bca with sides of length a, b, and c. perpendicular cd forms right triangles bdc and cda. cd measures h units, bd measures y units, da measures x units. the following two-column proof with missing justifications proves the pythagorean theorem using similar triangles: statement justification draw an altitude from point c to line segment ab let segment bc = a segment ca = b segment ab = c segment cd = h segment db = x segment ad = y y + x = c c over a equals a over y and c over b equals b over x a2 = cy; b2 = cx a2 + b2 = cy + b2 a2 + b2 = cy + cx a2 + b2 = c(y + x) a2 + b2 = c(c) a2 + b2 = c2 which is not a justification for the proof? pieces of right triangles similarity theorem side-side-side similarity theorem substitution addition property of equality

There is a misprint in the question.

In the statement you have written DB=x ,and DA=y but in Question you have written DA= x and DB=y.

So, let me just considering your Statement justification

Let segment BC = a, segment CA = b ,segment AB = c segment CD = h, segment DB = x, segment AD = y ,y + x = c

In Δ B DC and Δ BC A

∠B D C =∠B C A [each being 90°]

∠ B is common.

Δ B D C is similar to Δ BC A.

⇒ a² = c x  .........(1)

Similarly we can prove that

Δ ADC is similar to Δ BC A.

⇒b²= c y ......(2)

adding (1) and (2)

⇒

               =c×c [∴ x+y =c]

                 =c²

So, we have used two properties 1.  Right Triangles Similarity Theorem 2.Substitution Addition Property of Equality.

we haven't used  Side-Side-Side Similarity Theorem. It is not the right justification for the proof.

answer:  

step-by-step explanation:

here x represents the height of the pole,

and, the height of the shadow of the pole is 12 feet.

also, the angle of elevation from the top of the pole is 40°,

therefore,

by the low of sine,

which is the required equation for finding the value of x,

the answer is. -82562234434584

step-by-step explanation: