To solve this problem, we can use trigonometry, specifically the sine function.
Let's denote:
- \( h \) as the height of the kite above the child's hand.
- \( d \) as the distance between the ground and the child's hand.
- \( L \) as the length of the string.
a) To find the height of the kite above the child's hand (\( h \)), we can use the sine function:
\[ \sin(\text{angle}) = \frac{h}{L} \]
\[ h = L \times \sin(\text{angle}) \]
\[ h = 110 \times \sin(70^\circ) \]
\[ h \approx 104.148 \, \text{m} \]
So, the height of the kite above the child's hand is approximately 104.148 meters (to three significant figures).
b) To find the height of the kite from the ground, we need to add the height of the child's hand to the height of the kite above the child's hand:
\[ \text{Total height from ground} = h + d \]
\[ \text{Total height from ground} = 104.148 + 2.45 \]
\[ \text{Total height from ground} \approx 106.598 \, \text{m} \]
So, the height of the kite from the ground is approximately 106.598 meters (to five significant figures).
I can't show a picture, but you can imagine a right-angled triangle where the string is the hypotenuse, the angle is 70 degrees, and the height is what we are trying to find.
