Aplane 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 ?

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

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answer