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 about Shaina and the tree, we'll use trigonometric ratios, specifically the tangent function, which relates the angle of elevation, the distance from the observer to the base of the object, and the height of the object above the observer's line of sight.
Here's a step-by-step solution:
1. Convert Shaina’s Height to Feet:
Shaina is 5 feet 6 inches tall. First, convert her height entirely into feet. Since there are 12 inches in a foot, 6 inches is equivalent to 0.5 feet.
Therefore, Shaina’s height is:
[tex]\[
5 \text{ feet} + 0.5 \text{ feet} = 5.5 \text{ feet}
\][/tex]
2. Identify the Known Values:
- Distance from Shaina to the tree: 20 feet
- Angle of elevation: 68 degrees
3. Calculate the Height of the Tree Above Shaina's Eye Level:
Using the tangent of the angle of elevation, which is defined by [tex]\(\tan(\text{angle}) = \frac{\text{opposite}}{\text{adjacent}}\)[/tex], we can find the height of the tree above Shaina's line of sight. Here the "opposite" side is the height we wish to find, and the "adjacent" side is the distance from Shaina to the tree (20 feet).
[tex]\[
\text{height above eye level} = \tan(68^\circ) \times 20 \text{ feet}
\][/tex]
Using the trigonometric calculation, this gives approximately 49.5 feet.
4. Calculate the Total Height of the Tree:
The tree's total height is the sum of the height above Shaina’s eye level (49.5 feet) and Shaina’s total height (5.5 feet).
[tex]\[
\text{total height of the tree} = 49.5 \text{ feet} + 5.5 \text{ feet} = 55 \text{ feet}
\][/tex]
Therefore, the total height of the tree is approximately 55 feet.
Here's a step-by-step solution:
1. Convert Shaina’s Height to Feet:
Shaina is 5 feet 6 inches tall. First, convert her height entirely into feet. Since there are 12 inches in a foot, 6 inches is equivalent to 0.5 feet.
Therefore, Shaina’s height is:
[tex]\[
5 \text{ feet} + 0.5 \text{ feet} = 5.5 \text{ feet}
\][/tex]
2. Identify the Known Values:
- Distance from Shaina to the tree: 20 feet
- Angle of elevation: 68 degrees
3. Calculate the Height of the Tree Above Shaina's Eye Level:
Using the tangent of the angle of elevation, which is defined by [tex]\(\tan(\text{angle}) = \frac{\text{opposite}}{\text{adjacent}}\)[/tex], we can find the height of the tree above Shaina's line of sight. Here the "opposite" side is the height we wish to find, and the "adjacent" side is the distance from Shaina to the tree (20 feet).
[tex]\[
\text{height above eye level} = \tan(68^\circ) \times 20 \text{ feet}
\][/tex]
Using the trigonometric calculation, this gives approximately 49.5 feet.
4. Calculate the Total Height of the Tree:
The tree's total height is the sum of the height above Shaina’s eye level (49.5 feet) and Shaina’s total height (5.5 feet).
[tex]\[
\text{total height of the tree} = 49.5 \text{ feet} + 5.5 \text{ feet} = 55 \text{ feet}
\][/tex]
Therefore, the total height of the tree is approximately 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
