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 :
To solve the problem of finding the height of the tree using trigonometry, we can follow these steps:
1. Understand the scenario:
- Shaina is 5 feet, 6 inches tall. Since there are 12 inches in a foot, we convert her height entirely into feet: [tex]\(5 + \frac{6}{12} = 5.5\)[/tex] feet.
- She is 20 feet away from the tree.
- The angle of elevation from her line of sight to the bird at the top of the tree is 68 degrees.
2. Set up the trigonometric relation:
- We use the tangent of the angle of elevation because it relates the height opposite the angle (the difference in height between Shaina's eyes and the top of the tree) to the adjacent side (the distance from Shaina to the tree).
- The formulation will be:
[tex]\[
\tan(\text{angle}) = \frac{\text{opposite}}{\text{adjacent}}
\][/tex]
- Here, the angle is 68 degrees, the opposite side is the height of the tree above Shaina's height, and the adjacent side is 20 feet.
3. Calculate the height of the tree:
- First, convert the angle from degrees to radians as the tangent function uses radians: [tex]\(68\)[/tex] degrees [tex]\(\approx 1.19\)[/tex] radians.
- Rearrange the formula to find the total height of the tree:
[tex]\[
\text{tree height} = \tan(\text{68 degrees}) \times 20 + \text{Shaina's height}
\][/tex]
- Calculate [tex]\(\tan(68 \text{ degrees})\)[/tex], multiply by the distance (20 feet), and then add Shaina's height (5.5 feet).
4. Result:
- With these calculations, the height of the tree is approximately 55 feet.
Therefore, the height of the tree is about 55 feet.
1. Understand the scenario:
- Shaina is 5 feet, 6 inches tall. Since there are 12 inches in a foot, we convert her height entirely into feet: [tex]\(5 + \frac{6}{12} = 5.5\)[/tex] feet.
- She is 20 feet away from the tree.
- The angle of elevation from her line of sight to the bird at the top of the tree is 68 degrees.
2. Set up the trigonometric relation:
- We use the tangent of the angle of elevation because it relates the height opposite the angle (the difference in height between Shaina's eyes and the top of the tree) to the adjacent side (the distance from Shaina to the tree).
- The formulation will be:
[tex]\[
\tan(\text{angle}) = \frac{\text{opposite}}{\text{adjacent}}
\][/tex]
- Here, the angle is 68 degrees, the opposite side is the height of the tree above Shaina's height, and the adjacent side is 20 feet.
3. Calculate the height of the tree:
- First, convert the angle from degrees to radians as the tangent function uses radians: [tex]\(68\)[/tex] degrees [tex]\(\approx 1.19\)[/tex] radians.
- Rearrange the formula to find the total height of the tree:
[tex]\[
\text{tree height} = \tan(\text{68 degrees}) \times 20 + \text{Shaina's height}
\][/tex]
- Calculate [tex]\(\tan(68 \text{ degrees})\)[/tex], multiply by the distance (20 feet), and then add Shaina's height (5.5 feet).
4. Result:
- With these calculations, the height of the tree is approximately 55 feet.
Therefore, the height of the tree is about 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
