Question

A summer camp counselor wants to find a length x in feet across a lake as represented in the sketch to the left

Answer 1

The question is incomplete and without a picture. I found similar question as follows:

A summer camp counselor wants to find a length, x, in feet, across a lake as represented in the sketch above. The lengths represented by AB, EB, BD and CD on the sketch were determined to be 1800 feet, 1400 feet, 700 feet, and 800 feet, respectively. Segments AC and DE intersect at B, and the angle AEB and the angle CBD have the same measure. What is the value of x?

Answer:

1600ft

Step-by-step explanation:

Angle AEB and CBD is the same value.

Referring to the picture, since ABC and DBE are straight lines and crosses each other at B, the angle DBC and EBA are equal.

Since we have 2 equal angle, the third angle must be the same as well.

Therefore we can conclude that both ABE and CBD are similar triangle but with different factor with;

AB similar to BC

EB similar to BD

AE similar to CD

To find the factor between ABE and CBD,

EB / BD = 1400 / 700 = 2

So x, which is AE must be a factor of 2 to CD

AE = 2*800 =1600ft