We appreciate your visit to A tiger that is 20 inches tall casts a shadow that is 45 inches long The person walking the tiger is 68 inches tall How. This page offers clear insights and highlights the essential aspects of the topic. Our goal is to provide a helpful and engaging learning experience. Explore the content and find the answers you need!
Answer :
Sure! Let's solve the problem step by step.
We are given the following information:
1. The height of the tiger is 20 inches.
2. The shadow of the tiger is 45 inches.
3. The height of the person is 68 inches.
We need to find the length of the person's shadow. To solve this, we can use the concept of similar triangles. Similar triangles have the same shape but different sizes, and corresponding sides of similar triangles are proportional.
### Step-by-Step Solution:
1. Identify the known ratios:
- The ratio of the tiger's height to its shadow is [tex]\( \frac{20}{45} \)[/tex].
2. Express this ratio:
- [tex]\( \frac{\text{Height of the tiger}}{\text{Shadow of the tiger}} = \frac{20}{45} \)[/tex]
3. Set up the same ratio for the person:
- Since the triangles are similar, the ratio of the height of the person to the shadow of the person will be the same.
- Let [tex]\( x \)[/tex] be the length of the person's shadow. We can set up the proportion as:
[tex]\[
\frac{\text{Height of the person}}{\text{Shadow of the person}} = \frac{\text{Height of the tiger}}{\text{Shadow of the tiger}}
\][/tex]
[tex]\[
\frac{68}{x} = \frac{20}{45}
\][/tex]
4. Solve for [tex]\( x \)[/tex]:
- Cross-multiply to solve for [tex]\( x \)[/tex]:
[tex]\[
68 \times 45 = 20 \times x
\][/tex]
[tex]\[
3060 = 20x
\][/tex]
[tex]\[
x = \frac{3060}{20}
\][/tex]
[tex]\[
x = 153
\][/tex]
The length of the person's shadow is 153 inches.
We are given the following information:
1. The height of the tiger is 20 inches.
2. The shadow of the tiger is 45 inches.
3. The height of the person is 68 inches.
We need to find the length of the person's shadow. To solve this, we can use the concept of similar triangles. Similar triangles have the same shape but different sizes, and corresponding sides of similar triangles are proportional.
### Step-by-Step Solution:
1. Identify the known ratios:
- The ratio of the tiger's height to its shadow is [tex]\( \frac{20}{45} \)[/tex].
2. Express this ratio:
- [tex]\( \frac{\text{Height of the tiger}}{\text{Shadow of the tiger}} = \frac{20}{45} \)[/tex]
3. Set up the same ratio for the person:
- Since the triangles are similar, the ratio of the height of the person to the shadow of the person will be the same.
- Let [tex]\( x \)[/tex] be the length of the person's shadow. We can set up the proportion as:
[tex]\[
\frac{\text{Height of the person}}{\text{Shadow of the person}} = \frac{\text{Height of the tiger}}{\text{Shadow of the tiger}}
\][/tex]
[tex]\[
\frac{68}{x} = \frac{20}{45}
\][/tex]
4. Solve for [tex]\( x \)[/tex]:
- Cross-multiply to solve for [tex]\( x \)[/tex]:
[tex]\[
68 \times 45 = 20 \times x
\][/tex]
[tex]\[
3060 = 20x
\][/tex]
[tex]\[
x = \frac{3060}{20}
\][/tex]
[tex]\[
x = 153
\][/tex]
The length of the person's shadow is 153 inches.
Thanks for taking the time to read A tiger that is 20 inches tall casts a shadow that is 45 inches long The person walking the tiger is 68 inches tall How. We hope the insights shared have been valuable and enhanced your understanding of the topic. Don�t hesitate to browse our website for more informative and engaging content!
- Why do Businesses Exist Why does Starbucks Exist What Service does Starbucks Provide Really what is their product.
- The pattern of numbers below is an arithmetic sequence tex 14 24 34 44 54 ldots tex Which statement describes the recursive function used to..
- Morgan felt the need to streamline Edison Electric What changes did Morgan make.
Rewritten by : Barada
