A plane flying at a certain altitude is observed from two points that are 3 miles apart. The angles of elevation made by two points are 55 and 72, as seen in the diagram. The altitude of the plane to the nearest tenth of a mile is ?

Answer:The altitude of the plane is 8 milesStep-by-step explanation:see the attached figure to better understand the problemwe know thatIn the right triangle ABCtan(72°)=h/xh=xtan(72°) -----> equation AIn the right triangle ABDtan(55°)=h/(x+3)h=(x+3)tan(55°) -----> equation Bequate equation A and equation B and solve for xxtan(72°)=(x+3)tan(55°)xtan(72°)-xtan(55°)=3tan(55°)x[tan(72°)-tan(55°)]=3tan(55°)x=3tan(55°)/[tan(72°)-tan(55°)]Find the value of hh=xtan(72°)h=[3tan(55°)*tan(72°)]/[tan(72°)-tan(55°)]h=8 miles