41 If it is given that \[ \sin 30^{\circ}=\frac{1}{2} \text { Cos } 30^{\prime}=\frac{4}{2} \] Use your knowedge of trigonometry to determine the foltowing Peter stands at C with his Kite. The string of the kite is 20 m long How high is the kite above the ground? (Determine the length of AB .)

To solve the problem, we need to determine the height of the kite above the ground, which can be represented as the vertical distance from point A (the kite) to point B (the ground). Given: - The length of the string (AC) is 20 m. - The angle at point C (the angle between the string and the horizontal ground) is \(30^{\circ}\). We can use the sine function to find the height (AB) of the kite above the ground. The sine of an angle in a right triangle is defined as the ratio of the length of the opposite side to the hypotenuse. ### Step 1: Identify the relationship In triangle ABC: - \(AB\) is the height of the kite above the ground. - \(AC\) is the length of the string (hypotenuse). - The angle \(C\) is \(30^{\circ}\). Using the sine function: \[ \sin(C) = \frac{AB}{AC} \] ### Step 2: Substitute known values Substituting the known values into the equation: \[ \sin(30^{\circ}) = \frac{AB}{20} \] ### Step 3: Calculate \(AB\) We know that: \[ \sin(30^{\circ}) = \frac{1}{2} \] So we can substitute this value into the equation: \[ \frac{1}{2} = \frac{AB}{20} \] ### Step 4: Solve for \(AB\) To find \(AB\), we can rearrange the equation: \[ AB = 20 \cdot \frac{1}{2} \] \[ AB = 10 \] ### Conclusion The height of the kite above the ground is \(10\) m.