Kite Height 08941B
1. **Problem statement:** Kristoffer's kite string makes an angle of 15° with the ground, and the string length is $\sqrt{6} + \sqrt{2}$ meters. We need to find how high the kite is above the ground.
2. **Formula used:** The height of the kite corresponds to the vertical component of the string length. Using trigonometry, height $h = \text{string length} \times \sin(\theta)$ where $\theta = 15^\circ$.
3. **Calculate the height:**
$$
h = (\sqrt{6} + \sqrt{2}) \times \sin(15^\circ)
$$
4. **Evaluate $\sin(15^\circ)$:**
$$
\sin(15^\circ) = \sin(45^\circ - 30^\circ) = \sin 45^\circ \cos 30^\circ - \cos 45^\circ \sin 30^\circ
$$
Using known values:
$$
= \frac{\sqrt{2}}{2} \times \frac{\sqrt{3}}{2} - \frac{\sqrt{2}}{2} \times \frac{1}{2} = \frac{\sqrt{6}}{4} - \frac{\sqrt{2}}{4} = \frac{\sqrt{6} - \sqrt{2}}{4}
$$
5. **Substitute back:**
$$
h = (\sqrt{6} + \sqrt{2}) \times \frac{\sqrt{6} - \sqrt{2}}{4}
$$
6. **Simplify the product:**
$$
(\sqrt{6} + \sqrt{2})(\sqrt{6} - \sqrt{2}) = (\sqrt{6})^2 - (\sqrt{2})^2 = 6 - 2 = 4
$$
7. **Calculate height:**
$$
h = \frac{4}{4} = 1
$$
**Final answer:** The kite is 1 meter above the ground.