To find the height of Jamila's kite, we can visualize the situation as a right triangle. The string forms the hypotenuse of the triangle, the height of the kite above the ground is one leg, and the distance from the point directly beneath the kite on the ground to where Jamila is standing is the other leg.
Given:
- The length of the string (hypotenuse) is 22 feet.
- The elevation above the ground where Jamila is holding the string is 3 feet.
- The angle of elevation is 45°.
In this case, we can find the height of the kite above the ground using the properties of the triangle. The angle of elevation implies that the segments of the triangle are related in such a way that:
- The vertical leg (height from the level of Jamila’s hands to the kite) can be calculated using trigonometry.
- The horizontal leg will also be equal to the vertical leg since it's a 45° angle triangle (45°-45°-90° triangle).
Let's denote:
- \( H \) as the height of the kite above the ground,
- The height of Jamila’s hand above the ground is 3 feet.
From the 45° angle rule in a 45°-45°-90° triangle:
- Height gained through the string = Horizontal distance
- So, if we let \( x \) be the height increase above where she is holding the string, we can say:
\[ H - 3 = x \]
Using the formula for the hypotenuse in a right triangle, we have:
\[ x = 22 \times \sin(45^\circ) \] Since \( \sin(45^\circ) = \frac{\sqrt{2}}{2} \):
\[ x = 22 \times \frac{\sqrt{2}}{2} = 11\sqrt{2} \approx 15.556 \]
Now, substitute \( x \) back into the height equation:
\[ H - 3 = 11\sqrt{2} \]
Thus,
\[ H = 3 + 11\sqrt{2} \approx 3 + 15.556 \approx 18.556 \]
Rounding to the nearest tenth gives us:
\[ H \approx 18.6 \text{ feet} \]
Therefore, the height of Jamila’s kite above the ground is approximately 18.6 feet.