A kite on a 160-foot string is caught on a pole. When the full length of the string is stretched in a straight line to the ground, it touches the ground a distance of 50 feet from the bottom of the pole. The string forms an angle of _______° with the ground when it is stretched like this.
Accepted Solution
A:
Answer:String form an angle of 18.2° with the ground.Step-by-step explanation:Given: Length of the string of a kite = 160 ft. Kite stuck on pole at height of = 50 ft.We need to find: Measure of angle formed by string of kite with ground.Attached figure showing the given situation.let α be the required angle.In ΔABC,using trigonometric ratio,[tex]sin\,\aplha=\frac{AB}{AC}[/tex][tex]sin\,\aplha=\frac{50}{160}[/tex][tex]sin\,\aplha=\frac{5}{16}[/tex][tex]sin\,\aplha=0.3125[/tex][tex]\aplha=sin^{-1}(0.3125)[/tex][tex]\alpha=18.20995686428301[/tex][tex]\alpha=18.21[/tex]Therefore, String form an angle of 18.2° with the ground.