A plane flying at a certain altitude is observed from two points that are 3 miles apart. The angles of elevation made by two poi
nts are 55 and 72, as seen in the diagram. The altitude of the plane to the nearest tenth of a mile is ?
2 answers:
Answer:
The altitude of the plane is 8 miles
Step-by-step explanation:
see the attached figure to better understand the problem
we know that
<u>In the right triangle ABC</u>
tan(72°)=h/x
h=xtan(72°) -----> equation A
<u>In the right triangle ABD</u>
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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