A tunnel must be made through a hill. As a result, a surveyor and an engineer create a sketch of the area. The sketch, displayed below, includes information they have either researched or measured. They need to build a tunnel from the point E to the point H on the sketch. a) Prove the three triangles ΔSFH, ΔEGL, and ΔSIL are similar. b) Use similar triangles to determine the length from H to E.

a) Look step by step explanation

b) x = 498,22

Step-by-step explanation:

a) Two triangles are similar if all their angles are equal

Then in Δ SFH  and  Δ GEL we got:

∡ SFH = ∡ EGL   right angles

∡ LEG = ∡ HSF   since the same straight line (SL) is cut by parallel lines (vertical  segments  EG and SF )

∡ SHF = ∡ ELG  The same straight line SL is cut by two parallel segments FH and GL  ( horizontal segments)

The Δ SIL is similar to the two previous Δs according to:

∡ SIL is a right angle

∡ ILS = ∡ GLE = ∡ FHS

∡ ISL = ∡FSH = ∡GEL

The condition for similar triangles is satisfied

b)

From Δs    FSH and  GEL

SF/EG  = 380/EL

225/180  =  380/EL

225*EL  =  180*380

EL = 180*380/225

EL = 304

From Δs  SIL and SFH

225/ (225 +475)  =  380/ (380 + x + 304)

225 / 700  = 380 / 684 + x

225 * ( 684 + x ) = 700*380

153900 + 225*x = 266000

225*x = 266000 - 153900

225*x = 112100

x = 498,22

google dat sis

step-by-step explanation: