Question

In the diagram to the left, \angle ABC∠ABCangle, A, B, C and \angle DCB∠DCBangle, D, C, B are right angles. Which of the following is closest to the length of \overline{DE}
DE
start overline, D, E, end overline?

Answer 1

Step-by-step explanation:

ABC and DCB are right angles . . .

<mumble mumble>

Prove that angle ABC is equal to angle DCB

Duh. They are both right angles.

In the diagram to the left, \angle ABC∠ABCangle, A, B, C and \angle DCB∠DCBangle, D, C, B are right angles. Which of the following is closest to the length of \overline{DE}

DE

hope it helps you

Answer 2

The length of DE is 38.252.

Given:

Two triangles as shown in the figure below.

To Find:

the length of DE

Solution:

In triangle ABE,

∠A = x

∠B = 90°

⇒ ∠AEB = 180 - 90 - x = (90 - x)

Similarly, in triangle DEC,

∠C = 90°

∠DEC = 90 - x

⇒ ∠EDC = 180 - 90 - 90 + x = x

Now, by AAA similarity criterion, we can see that triangles ABE and DCE are similar.

Thus, the ratio of their sides will also be equal

⇒ BE/CE = AE/DE

5/13.1 = 14.6/DE

DE = (14.6 × 13.1)/5

DE = 191.26/5

DE = 38.252

Thus, the length of DE is 38.252.

#SPJ2