We appreciate your visit to Use trigonometric ratios to solve the following problem Shaina who is 5 feet 6 inches tall is standing 20 feet from the base of a. 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 using trigonometry.
1. Understand the problem:
Shaina is observing a woodpecker at the top of a tree. She is 5 feet 6 inches tall and standing 20 feet away from the base of the tree. The angle of elevation from her line of sight to the bird is 68 degrees. We need to find the height of the tree.
2. Convert Shaina's height to feet:
Since Shaina's height is given in feet and inches, we need to convert this to feet only for easier calculations:
- 5 feet 6 inches = 5 + 6/12 feet = 5.5 feet.
3. Use trigonometric ratios:
The angle of elevation, the distance from the tree, and the height above Shaina's eye level form a right triangle. We can use the tangent function, which is the ratio of the opposite side (height of the tree above her eye level) to the adjacent side (distance from the tree).
[tex]\[
\tan(\theta) = \frac{\text{opposite}}{\text{adjacent}}
\][/tex]
Where:
- [tex]\(\theta = 68^\circ\)[/tex]
- opposite = height of the tree above Shaina's head level.
- adjacent = 20 feet.
4. Solve for the height of the tree above Shaina's head level:
[tex]\[
\tan(68^\circ) = \frac{\text{height above}}{20}
\][/tex]
Solving for the height above:
[tex]\[
\text{height above} = 20 \times \tan(68^\circ)
\][/tex]
Calculate [tex]\(\tan(68^\circ)\)[/tex] and then the height above.
5. Find the total height of the tree:
Add Shaina's height to the height above her head level to find the total height:
[tex]\[
\text{Total height} = \text{Shaina's height} + \text{height above her head}
\][/tex]
[tex]\[
\text{Total height} = 5.5 + \text{height above}
\][/tex]
6. Convert the total height to inches (if necessary):
Since some of the answer choices are in inches, convert feet to inches:
[tex]\[
\text{Total height in inches} = \text{Total height in feet} \times 12
\][/tex]
Using the calculations, the total height of the tree is approximately 55 feet or 660 inches. Therefore, the answer that makes the most sense from the provided choices is 55 feet.
1. Understand the problem:
Shaina is observing a woodpecker at the top of a tree. She is 5 feet 6 inches tall and standing 20 feet away from the base of the tree. The angle of elevation from her line of sight to the bird is 68 degrees. We need to find the height of the tree.
2. Convert Shaina's height to feet:
Since Shaina's height is given in feet and inches, we need to convert this to feet only for easier calculations:
- 5 feet 6 inches = 5 + 6/12 feet = 5.5 feet.
3. Use trigonometric ratios:
The angle of elevation, the distance from the tree, and the height above Shaina's eye level form a right triangle. We can use the tangent function, which is the ratio of the opposite side (height of the tree above her eye level) to the adjacent side (distance from the tree).
[tex]\[
\tan(\theta) = \frac{\text{opposite}}{\text{adjacent}}
\][/tex]
Where:
- [tex]\(\theta = 68^\circ\)[/tex]
- opposite = height of the tree above Shaina's head level.
- adjacent = 20 feet.
4. Solve for the height of the tree above Shaina's head level:
[tex]\[
\tan(68^\circ) = \frac{\text{height above}}{20}
\][/tex]
Solving for the height above:
[tex]\[
\text{height above} = 20 \times \tan(68^\circ)
\][/tex]
Calculate [tex]\(\tan(68^\circ)\)[/tex] and then the height above.
5. Find the total height of the tree:
Add Shaina's height to the height above her head level to find the total height:
[tex]\[
\text{Total height} = \text{Shaina's height} + \text{height above her head}
\][/tex]
[tex]\[
\text{Total height} = 5.5 + \text{height above}
\][/tex]
6. Convert the total height to inches (if necessary):
Since some of the answer choices are in inches, convert feet to inches:
[tex]\[
\text{Total height in inches} = \text{Total height in feet} \times 12
\][/tex]
Using the calculations, the total height of the tree is approximately 55 feet or 660 inches. Therefore, the answer that makes the most sense from the provided choices is 55 feet.
Thanks for taking the time to read Use trigonometric ratios to solve the following problem Shaina who is 5 feet 6 inches tall is standing 20 feet from the base of a. 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
