Elevation angles

From the endpoints of the base 240 m long and inclined at an angle of 18° 15 ', the top of the mountain can be seen at elevation angles of 43° and 51°. How high is the mountain?

Correct answer:

h =  1174.9592 m

Step-by-step explanation:

a=240 m α=18+15/60=473=18.25  h1=a sin(α)=240 sin(18.25°)75.1593 m  cosα=x0:a  x0=a cos(α)=240 cos(18.25°)227.9278 m  β=43  γ=51   tanβ=(hh1):(x0+x) tanγ=h:x  tanβ=(x tanγh1):(x0+x)  (x0+x) tanβ=(x tanγh1) x0 tanβ+x tanβ=x tanγh1  x=tanγtanβh1+x0 tanβ=tan51° tan43° h1+x0 tan43° =tan51° tan43° 75.1593+227.9278 tan43° =1.2348970.93251575.1593+227.9278 0.932515=951.46321 m  h=x tanγ=x tan51° =951.4632 tan51° =951.4632 1.234897=1174.95922=1174.9592 m   Verifying Solution:  β1=π180°arctan(x0+xhh1)=π180°arctan(227.9278+951.46321174.959275.1593)=43  γ1=π180°arctan(h/x)=π180°arctan(1174.9592/951.4632)=51 

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