QuestionA man is $2 \mathrm{~cm}$ tall in a photo and $1.8 \mathrm{~m}$ tall in reality. Find the scale factor.

Studdy Solution

STEP 1

Assumptions1. The man in the photograph is cm tall. . His actual height is1.8 m.
3. We need to find the scale factor and write a scale statement. 4.1 m =100 cm.

STEP 2

First, we need to convert the actual height of the man from meters to centimeters, as the height in the photograph is given in centimeters.
$Actual\, height\, in\, cm = Actual\, height\, in\, m \\times100$

STEP 3

Now, plug in the given value for the actual height in meters to calculate the actual height in centimeters.
$Actual\, height\, in\, cm =1.8\, m \\times100$

STEP 4

Calculate the actual height in centimeters.
$Actual\, height\, in\, cm =1.8\, m \\times100 =180\, cm$

STEP 5

Now that we have the actual height in centimeters, we can find the scale factor. The scale factor is the ratio of the height in the photograph to the actual height.
$Scale\, factor = Height\, in\, photograph / Actual\, height$

STEP 6

Plug in the values for the height in the photograph and the actual height to calculate the scale factor.
$Scale\, factor =2\, cm /180\, cm$

STEP 7

Calculate the scale factor.
$Scale\, factor =2\, cm /180\, cm =0.0111$

STEP 8

The scale statement is written as1actual size. In this case, the actual size is the reciprocal of the scale factor.
$Actual\, size =1 / Scale\, factor$

STEP 9

Plug in the value for the scale factor to calculate the actual size.
$Actual\, size = /.011$

STEP 10

Calculate the actual size.
$Actual\, size = /0.011 =90$ The scale statement is90 and the scale factor is0.011.

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