Nasim is flying a kite, holding his hands a distance of 2.5 feet above the ground and letting all the kite’s string play out. He measures the angle of elevation from his hand to the kite to be 28degrees ∘ . If the string from the kite to his hand is 105 feet long, how many feet is the kite above the ground? Round your answer to the nearest hundredth of a foot if necessary.

To solve this problem, we can use trigonometry. Specifically, we'll use the sine function, which is defined as the ratio of the length of the side opposite the angle to the length of the hypotenuse in a right triangle.

Here, the angle of elevation is 28 degrees, the length of the hypotenuse (the kite string) is 105 feet, and we want to find the length of the side opposite the angle, which represents the height of the kite above Nasim's hands.

The sine of an angle is calculated as:

sin(angle) = opposite/hypotenuse

Rearranging the formula to solve for the opposite side gives:

opposite = sin(angle) * hypotenuse

Substituting the given values into the formula gives:

opposite = sin(28 degrees) * 105 feet

Calculating this gives approximately 49.42 feet. This is the height of the kite above Nasim's hands.

However, we're asked for the height of the kite above the ground. Since Nasim's hands are 2.5 feet above the ground, we need to add this to the height above his hands to get the total height above the ground:

Total height = height above hands + height of hands above ground Total height = 49.42 feet + 2.5 feet = 51.92 feet

So, the kite is approximately 51.92 feet above the ground.