In the diagram, the base of the tower is at point h, and the top of the tower is at point f. if the distance from the base of the tower to point g is 7x feet and the distance from the base of the tower to point e is 6x + 12 feet, find ge, the distance across the lake. a. 84 feet b. 94 feet c. 168 feet d. 186 feet

In the diagram, the base of the tower is at point H, and the top of the tower is at point F. If the distance from the base of the tower to point G is 7x feet and the distance from the base of the tower to point E is 6x + 12 feet, find GE, the distance across the lake.
This problem can be solved using triangle similarities:

Consider the Pythagorean Theorem with the formula; c^2=a^2+b^2
let: a=height from base to point
      b1=base of the first triangle formed
      b2-base of the second triangle formed
      c1=c2= hypotenuse of the two triangles,
note:
they have equal hypotenuse and share the same height, thus a1=a2

sqrt[(a^2+(7x)^2)]=sqrt[a^2+(6x+12)^2]
sqrt(49x^2) =sqrt[(6x+12)^2]
7x=6x+12
x=12

GE=7x+6x+12
GE=7(12)+6(12)+12
GE= 168 feet

Thus, the answer is:
C.168 feet

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