A new bridge structure requires triangles that are in a ratio of 1:1. If AC = 2x + 10 and EC = 4x − 18, find the distance between the top and bottom of the bridge, in feet.

Distance between the top and bottom of the bridge is 76 feet

Solution:

The image of the question is attached below.

Ratio of the triangles is 1 : 1.

AC = 2x + 10 and EC = 4x − 18.

Since the two triangles ACB and DCE are in the ratio 1 : 1, so their corresponding sides are also in the ratio 1 : 1.

Therefore sides AC and EC are corresponding to each other.

AC : EC = 1 : 1

Subtract 10 from both sides of the equation.

Subtract 4x from both sides of the equation.

Divide by -2 on both sides, we get

⇒ x = 14

Distance between the top and bottom of the bridge is EA.

EA = AC + EC

     = 2x + 10 + 4x - 18

     = 6x - 8

     = 6(14) - 8

     = 84 - 8

EA = 76 feet

Distance between the top and bottom of the bridge is 76 feet.

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,

answer: there are x+184 pages in olivia's book.

step-by-step explanation:

let the total number of pages in the book which olive has already read be x.

then if olive has 184 pages left to read, then the total number of pages are in olive's book= pages she has read+pages she has left to read

therefore, the total number of pages in olivia's book=

hence, there are x+184 pages in olivia's book.