Trigonometry Question

[5riti]

At the foot of a mountain, the elevation of its summit is 45. After ascending 1 km towards the mountain up an incline of 30, the elevation changes to 60. Find the height of the mountain.

[kiran_ghosh]

given:- /_acb=45
/__ocb=30
/___aoe=60
oc=1 km

required to find= Height=AE




proof:--
od/oc= sin30=1/2
oc=1 Km thus, od=1/2 km

od=eb=1/2 km

dc/oc=cos 30 = root3 /2
oc= 1 Km thus dc= root 3 /2



let oe=x km
oe=db=x km

ae/oe =tan 60=root3
ae/x=root3
thus ae=root 3 x


ab/bc=tan 45

thus ab=bc
ab=ae+eb= root3x + 1/2
bc=bd+dc=x +root3/2
thus
root3x + 1/2 = x +root3/2
[2root3x + 1]/2 =[2x +root3]/2
2root3x + 1=2x +root3
2root3x -2x=root3-1
2x (root3-1)=root3-1
2x=1
x=1/2

now height=ab=ae+eb=root3x+1/2
=root3/2 + 1/2
=[root3 +1]/2
approx=1.366 Km


thats it hope its not confusin

dunno how to type angle or root
lolz