Johnny uses a mirror placed on level ground to measure the height of a building. Johnny's eyes are 6 feet above the ground and he stands 4 feet away from the mirror. From that distance, Johnny is able to see the top of the building in the mirror as shown in the diagram below.

If the mirror is 45 feet 3 inches away from the building’s base, how tall is the building?

To explain your reasoning, answer in complete sentences and include all relevant calculations.

The answer to your question is  B = 67.9 ft

Step-by-step explanation:

Data

Johnny's eyes height = J = 6 ft

distance from Johnny's to the mirror = dJ = 4 ft

distance from the mirror to the building = dB = 45 ft 3 in

building's height = B = ?

To solve this problem use the Thales' theorem. We can use this theorem because the triangles formed are similar.

                           B/ dB = 6/4

-Convert 3 in to ft

                 1 ft 12 in

                 x      3 in

                 x = (3 x 1)/12

                 x = 0.25 ft

dB = 45 + 0.25

     = 45.25 ft

-Substitution

                       B / 45.25 = 6/4

-Solve for B

                       B = 6(45.25) / 4

-Simplification

                       B = 271.5/4

-Result

                       B = 67.9 ft

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