Q:

Francesca is looking at an airplane. She measures the angle at which she is looking up and finds it to be 55 degrees. If the airplane is traveling at an altitude of 30000 feet, about how far is the airplane from Francesca?A. 21,006 feetB. 36,623 feetC. 45,043 feet D. 53,303 feet

Accepted Solution

A:
Answer:Option: B is the correct answer.                     B. 36,623 feetStep-by-step explanation:The angle of elevation is: 55 degreeWe model this problem by taking a right angled triangle such that the side opposite to the 55 degree is of length 30000 feet.Now let us consider x denote the distance of the plane from Francesa.i.e. x denote the hypotenuse of the right angled triangle.Hence, in right angled triangle i.e. ΔABC we have:[tex]\sin 55=\dfrac{30000}{x}\\\\i.e.\\\\x=\dfrac{30000}{\sin 55}\\\\i.e.\\\\x=\dfrac{30000}{0.81915}\\\\\\i.e.\\\\\\x=36623.2376\ feet[/tex]Round to the nearest feet we get: x=36,623 feet