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The problem describes Jarrod flying a kite with a string of 70 meters, initially at a 40° angle to the horizontal. After a gust of wind, the kite string's angle increases to 50°. We need to calculate how much higher the kite is after this change in angle.

### Step 1: Calculate the kite's initial height
The height of the kite can be calculated using trigonometry. The vertical height of the kite is the opposite side of the right triangle formed by the string, so we can use the sine function.

The formula for the height \( h \) is:

\[
h = L \times \sin(\theta)
\]

Where:
- \( L = 70 \, \text{m} \) (the length of the string),
- \( \theta = 40^\circ \) (initial angle).

Substituting values:

\[
h_{\text{initial}} = 70 \times \sin(40^\circ)
\]

### Step 2: Calculate the new height
Now we calculate the height after the string is at a 50° angle:

\[
h_{\text{new}} = 70 \times \sin(50^\circ)
\]

### Step 3: Determine the change in height
The change in height is the difference between the new height and the initial height:

\[
\Delta h = h_{\text{new}} - h_{\text{initial}}
\]

Now, I'll calculate these values for you.The results are as follows:

- The initial height of the kite above the ground was **4499.51 cm** (or 44.995 meters).
- The new height after the gust of wind is **5362.31 cm** (or 53.623 meters).
- The kite is now **862.8 cm** (or 8.628 meters) higher than before.

Would you like a more detailed breakdown, or do you have any other questions?

### Related Questions:
1. How does the sine function relate to calculating heights in right-angled triangles?
2. What is the difference between sine and cosine when calculating triangle properties?
3. How would the problem change if the string length were doubled?
4. What if the string's angle increased to 60° instead of 50°?
5. How do you convert degrees to radians for trigonometric calculations?

### Tip:
Always ensure your calculator is in the correct mode (degrees or radians) based on the angle unit used in your calculations.

Jarrod is flying a kite in the park. The kite is on the end of a string that is 70m long and at an angle of 40° with the horizontal ground. Suddenly, a gust of wind blows the kite up higher so that the string makes an angle of 50° with the ground. How much higher is the kite above the ground now, compared to its original height? Show all working, and give your answer to the nearest centimetre.

Solve a trigonometry problem involving the height of a kite. The kite string is 70m long and changes angles from 40° to 50°. Learn how to calculate the height difference using sine function in a right-angled triangle. Suitable for students in Grades 9-12.

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