Kaj is flying a kite, holding her hands a distance of 3.5 feet above the ground and letting all the kite's string play out. She measures the angle of elevation from her hand to the kite to be 33^circ .If the string from the kite to her hand is 75 feet long, how many feet is the kite above the ground? Round your answer to the nearest hundredth of a foot if necessary. Answer Attemptiout of 2 square feet

## Step 1<br />In this problem, we are dealing with a right triangle. The string from Kaj's hand to the kite forms the hypotenuse of the triangle, the height of the kite from Kaj's hand forms the opposite side, and the distance from Kaj's hand to the ground forms the adjacent side.<br /><br />## Step 2<br />We are given the length of the hypotenuse (75 feet) and the angle of elevation (33 degrees). We need to find the length of the opposite side, which is the height of the kite from Kaj's hand.<br /><br />## Step 3<br />We can use the sine function to find the length of the opposite side. The sine of an angle in a right triangle is defined as the ratio of the length of the opposite side to the length of the hypotenuse.<br /><br />### **The formula for the sine function is: \(sin(\theta) = \frac{opposite}{hypotenuse}\)**<br /><br />## Step 4<br />Substituting the given values into the formula, we get:<br /><br />### **\(sin(33) = \frac{opposite}{75}\)**<br /><br />## Step 5<br />Solving for the opposite side, we get:<br /><br />### **\(opposite = 75 * sin(33)\)**<br /><br />## Step 6<br />Calculating the above expression, we get approximately 44.22 feet.<br /><br />## Step 7<br />However, this is the height of the kite from Kaj's hand, not from the ground. We need to add the height of Kaj's hand from the ground (3.5 feet) to get the total height of the kite from the ground.<br /><br />## Step 8<br />Adding 3.5 feet to 44.22 feet, we get approximately 47.72 feet.