Questions: Hawa is flying a kite, holding her hands a distance of 3.75 feet above the ground and letting all the kite's string out. She measures the angle of elevation from her hand to the kite to be 26 degrees. If the string from the kite to her hand is 135 feet long, how many feet is the kite above the ground? Round your answer to the nearest tenth of a foot if necessary.

Solution Steps

We can represent the situation with a right triangle. The hypotenuse is the length of the string (135 ft). The angle of elevation from Hawa's hand to the kite is 26°. The vertical side of the triangle represents the kite's height above Hawa's hand.

Let \(h\) be the height of the kite above Hawa's hand. We can use the sine function to find \(h\):

\(\sin(26^\circ) = \frac{h}{135}\) \(h = 135 \cdot \sin(26^\circ)\) \(h \approx 135 \cdot 0.4384\) \(h \approx 59.184\)

Hawa's hand is 3.75 feet above the ground. So, the total height of the kite above the ground is the height from Hawa's hand to the kite plus the height of Hawa's hand from the ground:

Total height \(\approx 59.184 + 3.75\) Total height \(\approx 62.934\)

Since we need to round to the nearest tenth of a foot, the final answer is approximately 62.9 feet.

Final Answer