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Answer :
Sure! Let's go through the steps to solve this problem:
1. Convert Shaina's Height to Feet Only:
- Shaina's height is given as 5 feet, 6 inches. First, we need to convert her height entirely into feet.
- There are 12 inches in a foot, so we can convert 6 inches to feet like this:
[tex]\[
6 \text{ inches} = \frac{6}{12} \text{ feet} = 0.5 \text{ feet}
\][/tex]
- Therefore, Shaina's total height in feet is:
[tex]\[
5 \text{ feet} + 0.5 \text{ feet} = 5.5 \text{ feet}
\][/tex]
2. Distance From the Tree:
- Shaina is standing 20 feet away from the base of the tree.
3. Angle of Elevation:
- The angle of elevation to the bird is given as 68 degrees.
4. Calculate the Height of the Tree Above Shaina's Eye Level:
- To find the height of the tree above Shaina's eye level, we use the tangent of the angle of elevation.
- The tangent function relates the angle of elevation to the opposite side (height of the tree above Shaina's eye level) and the adjacent side (distance from the tree). The formula is:
[tex]\[
\tan(\text{angle}) = \frac{\text{height above Shaina}}{\text{distance from tree}}
\][/tex]
- Rearranging the formula to solve for the height above Shaina:
[tex]\[
\text{height above Shaina} = \tan(68^\circ) \times 20 \text{ feet}
\][/tex]
5. Height Calculation:
- Using a calculator or trigonometric tables, we find:
[tex]\[
\tan(68^\circ) \approx 2.4751
\][/tex]
- Therefore:
[tex]\[
\text{height above Shaina} = 2.4751 \times 20 \text{ feet} \approx 49.50 \text{ feet}
\][/tex]
6. Total Height of the Tree:
- Finally, the total height of the tree is the height above Shaina plus Shaina's height:
[tex]\[
\text{total height of the tree} = 49.50 \text{ feet} + 5.5 \text{ feet} = 55.00 \text{ feet}
\][/tex]
Therefore, the height of the tree is approximately 55 feet.
1. Convert Shaina's Height to Feet Only:
- Shaina's height is given as 5 feet, 6 inches. First, we need to convert her height entirely into feet.
- There are 12 inches in a foot, so we can convert 6 inches to feet like this:
[tex]\[
6 \text{ inches} = \frac{6}{12} \text{ feet} = 0.5 \text{ feet}
\][/tex]
- Therefore, Shaina's total height in feet is:
[tex]\[
5 \text{ feet} + 0.5 \text{ feet} = 5.5 \text{ feet}
\][/tex]
2. Distance From the Tree:
- Shaina is standing 20 feet away from the base of the tree.
3. Angle of Elevation:
- The angle of elevation to the bird is given as 68 degrees.
4. Calculate the Height of the Tree Above Shaina's Eye Level:
- To find the height of the tree above Shaina's eye level, we use the tangent of the angle of elevation.
- The tangent function relates the angle of elevation to the opposite side (height of the tree above Shaina's eye level) and the adjacent side (distance from the tree). The formula is:
[tex]\[
\tan(\text{angle}) = \frac{\text{height above Shaina}}{\text{distance from tree}}
\][/tex]
- Rearranging the formula to solve for the height above Shaina:
[tex]\[
\text{height above Shaina} = \tan(68^\circ) \times 20 \text{ feet}
\][/tex]
5. Height Calculation:
- Using a calculator or trigonometric tables, we find:
[tex]\[
\tan(68^\circ) \approx 2.4751
\][/tex]
- Therefore:
[tex]\[
\text{height above Shaina} = 2.4751 \times 20 \text{ feet} \approx 49.50 \text{ feet}
\][/tex]
6. Total Height of the Tree:
- Finally, the total height of the tree is the height above Shaina plus Shaina's height:
[tex]\[
\text{total height of the tree} = 49.50 \text{ feet} + 5.5 \text{ feet} = 55.00 \text{ feet}
\][/tex]
Therefore, the height of the tree is approximately 55 feet.
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