QQuestionAnatomy and Physiology
QuestionAnatomy and Physiology
# Similarity and Ratios
## Step-by-step guide:
$\checkmark$ Two or more figures are similar if the corresponding angles are equal, and the corresponding sides are in proportion.
## Examples:
1) A girl 160 cm tall, stands 360 cm from a lamp post at night. Her shadow from the light is 90 cm long. How high is the lamp post?
Write the proportion and solve for missing side.
$\frac{\text { Smaller triangle height }}{\text { Smaller triangle base }}=\frac{\text { Bigger triangle height }}{\text { Bigger triangle base }}$
$\Rightarrow \frac{90 \mathrm{~cm}}{160 \mathrm{~cm}}=\frac{90 + 360 \mathrm{~cm}}{x} \Rightarrow 90 x= 160 \times 450 \Rightarrow x= 800 \mathrm{~cm}$
2) A tree 32 feet tall casts a shadow 12 feet long. Jack is 6 feet tall. How long is Jack's shadow?
Write a proportion and solve for the missing number.
$\frac{32}{12}=\frac{6}{x} \rightarrow 32 x= 6 \times 12 = 72$
$32 x= 72 \rightarrow x=\frac{72}{32}= 2.25$ feet
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Step 1: Write down the given information and the proportion for the problem.
\frac{\text{Bigger triangle height}}{\text{Bigger triangle base}} = \frac{\text{Smaller triangle height}}{\text{Smaller triangle base}}
The given information is: - The height of the tree (bigger triangle) is 32 feet. - The length of the tree's shadow (base of the bigger triangle) is 12 feet. - Jack's height (smaller triangle) is 6 feet. - We need to find the length of Jack's shadow (x, the base of the smaller triangle). The proportion is:
Step 2: Plug the given values into the proportion and solve for the unknown.
x = \frac{6 \times 12}{32} = \frac{72}{32} = 2.25~\text{feet}
Cross-multiply to solve for x: Divide both sides by 32:
Final Answer
Jack's shadow is 2.25 feet long.
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