Question

A kite is flying 82 ft off the ground, and its string is pulled taut. The angle of elevation of the kite is 61°. Find the length ofthe string. Round your answer to the nearest tenth.

Answer 1

Step 1: Draw the triangle.

Step 2: Concept

Use the trigonometric ratio to find the length of the string.

`\begin{gathered} \sin \theta\text{ = }\frac{opposite}{\text{hypotenuse}} \\ \tan \theta\text{ = }\frac{\text{opposite}}{\text{adjacent}} \\ \cos \theta\text{ = }\frac{adjacent}{\text{hypotenuse}} \end{gathered}`

Step 3: Name the sides of the triangle

Hypotenuse = L side facing right angle

Opposite = 82 ft side facing given angle

Adjacent = ___ The third side.

Step 4: Apply the sine formula to find the length of the string.

`\begin{gathered} \sin \theta\text{ = }\frac{Opposite}{\text{Hypotenuse}} \\ \sin 61\text{ = }(82)/(L) \\ 0.8746\text{ = }(82)/(L) \\ \end{gathered}`

Next, cross multiply

`\begin{gathered} 0.8746L\text{ = 82} \\ \text{Divide through by 0.8746} \\ L\text{ = }(82)/(0.8746) \\ L\text{ = 93.8 ft} \end{gathered}`

Final answer

The length of the string = 93.8 ft