To determine how far off the ground Jordan is, we can apply trigonometry, specifically the tangent function, which relates the angles of a right triangle to the lengths of the opposite and adjacent sides.
Here is the detailed step-by-step solution:
1. Identify the Given Information:
- Distance from the base of the Ferris wheel to Jordan's mom: [tex]\( 38 \)[/tex] feet.
- Angle of elevation from Jordan's mom to Jordan: [tex]\( 73^\circ \)[/tex].
2. Set Up the Trigonometric Relationship:
- We are dealing with a right triangle where:
- The horizontal leg (adjacent side) is the distance from Jordan's mom to the base of the Ferris wheel: [tex]\( 38 \)[/tex] feet.
- The vertical leg (opposite side) is the height from the ground to where Jordan is on the Ferris wheel (the unknown height we need to find).
- The angle of elevation [tex]\( \theta \)[/tex] is [tex]\( 73^\circ \)[/tex].
3. Use the Tangent Function:
- The tangent of an angle in a right triangle is the ratio of the length of the opposite side to the length of the adjacent side:
[tex]\[
\tan(\theta) = \frac{\text{opposite}}{\text{adjacent}}
\][/tex]
- Here, we have:
[tex]\[
\tan(73^\circ) = \frac{\text{height from the ground to Jordan}}{38 \text{ feet}}
\][/tex]
4. Solve for the Height:
- Rearrange the equation to solve for the height:
[tex]\[
\text{height from the ground to Jordan} = 38 \text{ feet} \times \tan(73^\circ)
\][/tex]
5. Calculate the Height:
- Using the given angle [tex]\( 73^\circ \)[/tex], we find:
[tex]\[
\text{height from the ground to Jordan} = 38 \text{ feet} \times \tan(73^\circ)
\][/tex]
6. Result:
- After evaluating the above expression, it is found that:
[tex]\[
\text{height from the ground to Jordan} \approx 124.29 \text{ feet}
\][/tex]
Therefore, Jordan is approximately 124.29 feet off the ground.
