Question
Justin is riding in a hot air balloon, directly over Ben, who is standing on the ground. Justin spots Patti on the ground at an angle of depression of 27 degrees. The balloon rises 35m. Now the angle of depression to Patti is 36 degrees. How far is Patti from Ben?
Answers
h = initial balloon height , d = Patti/Ben distance
h / d = tan(27º) ... h / tan(27º) = d
(h + 35) / d = tan(36º) ... (h + 35) / tan(36º) = d
(h + 35) tan(27º) = h tan(36º) ... 35 tan(27º) = h [tan(36º) - tan(27º)]
solve for h , then substitute back to find d
h / d = tan(27º) ... h / tan(27º) = d
(h + 35) / d = tan(36º) ... (h + 35) / tan(36º) = d
(h + 35) tan(27º) = h tan(36º) ... 35 tan(27º) = h [tan(36º) - tan(27º)]
solve for h , then substitute back to find d
Related Questions
a balloon is rising vertically at the rate of 2 m/s. an observer is standing on the ground 100m away...
Karla is riding vertically in a hot air balloon, directly over a point P on the ground. Karla spots...
you are at a parade looking up at a large balloon floating directly above the street. you are 60 fee...
Justin rode his bicycle to a park located 4 2/3 miles from his house.he returned along the same rout...