Question

A plane flying at a certain altitude is observed from two points that are 2.2 meters apart. The angles of elevation made by the two points are 55º and 72º.
If the plane is to the east of both observation posts, the altitude of the plane is
A) 0.5
B)0.7
C)1.9
D) 5.9

Answer 1

$tan(72)= \frac{y}{x} ; tan(55)= \frac{y}{2.2 + x}$
$y=xtan(72);y=(2.2+x)tan(55)$
So we are to merge the two equations into one, since both of the equations are equal to y. a = b, b = c therefore, a = c.
$xtan(72)=2.2tan(55)+xtan(55)$
We are to isolate x.
$x[tan(72)-tan(55)]=2.2tan(55)$
$x=\frac{2.2tan(55)}{tan(72)-tan(55)}$
The value of x is approximately, 1.9047m
Then, substitute the value of x from $y=xtan(72)$
$y=1.9047tan(72)$
y = 5.862m
Round up, then the answer would be D.