Johnny uses a mirror placed on level ground to measure the height of a building. Johnny is 6 feet tall and 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?

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calculista calculista · Answer 1 · 2019-03-17T14:50:39+01:00

Answer:

The height of the building is [tex]67\ ft\ 10.5\ in[/tex]

Step-by-step explanation:

Remember that

[tex]1\ ft=12\ in[/tex]

so

[tex]45\ ft\ 3\ in=45+3/12=45.25\ ft[/tex]

Let

x-------> the height of the building

Using proportion

[tex]\frac{6}{4}=\frac{x}{45.25}\\ \\x=45.25*6/4\\ \\x= 67.875\ ft[/tex]

[tex]67.875\ ft=67\ ft\ (0.875*12)\ in=67\ ft\ 10.5\ in[/tex]

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psm22415 psm22415 · Answer 2 · 2022-02-25T05:10:50+01:00

The height of the building is 67.5 feet.

Given

Johnny uses a mirror placed on level ground to measure the height of a building.

Johnny is 6 feet tall and stands 4 feet away from the mirror.

The height of the building is determined by applying trigonometric identities.

Let, the height of the building be x.

Then,

The height of the building is given by;

[tex]\rm Tan \theta=\dfrac{6}{4}=\dfrac{h}{45}\\\\\dfrac{6}{4}=\dfrac{h}{45}\\\\ 45\times 6=h\times 4\\\\4h=270\\\\h=\dfrac{270}{4}\\\\h= 67.5[/tex]

Hence, the height of the building is 67.5 feet.

To know more about trigonometric identities click the link is given below.

https://brainly.com/question/20156187