a plane flying at a certian altitude is observed from two points that are 3 miles apart. the Angles of elevation made by the two points are 55deg and 72deg
The altitude of the plane is 8 miles Step-by-step explanation: see the attached figure to better understand the problem we know that In the right triangle ABC tan(72°)=h/x h=xtan(72°) -----> equation A In the right triangle ABD tan(55°)=h/(x+3) h=(x+3)tan(55°) -----> equation B equate equation A and equation B and solve for x xtan(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 h h=xtan(72°) h=[3tan(55°)*tan(72°)]/[tan(72°)-tan(55°)] h=8 miles
