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Question

Art  the foot of a mountain, the angle of elevation of  its summit is 45. After ascending 1 km towards the mountain up an incline of 30, the elevation changes to  60 (as shown in the given figure). Fin dthe height of the mountain. [Given : 3=1.73.]


Solution

\

(\frac{SD}{FD} = tan 45^\circ = 1 \Rightarrow SD = FD = h km\)

FSD=SFD=45

ASC=180(60+90)=30

FSC=(4530)=15 and SFA=15

SAF=180(15+15)=150

By the sine formula on DeltaSAF,we have

AFsinFSA=FSsinSAF1sin15=2hsin150=2h302sqrt2(31)=22h

[FS=h2+h2=2h and sin 15=(31)22]

h=1(3)1×(3+1)(3+1)=(3+1)2=(1.73+1)2=2.732=1.365km.

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