At the foot of mountain, the elevation of its summit is 450
. After ascending 1000 m
towards to mountain up a slope of 300
inclination, the elevation is found to be 600
.
Find
the height of the mountain.
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Answer:
Let P be the summit of the mountain and Q be the foot.
Let A be the first position and B the second position of observation.
BN and BM are ⊥s to PQ and AQ respectively.
Then AB=1000m=1km,
∠MAB=30
0
,∠MAP=45
0
,∠NBP=60
0
Now, ∠BAP=∠MAP−∠MAB=45
0
−30
0
=15
0
∠APB=∠APN−∠BPN=45
0
−30
0
=15
0
.........[∠BNP=90
∘
,∠BPN=90−60=30
∘
]
∴△ABP is isosceles and ∴AB=BP
But AB=1 kilometer, ∴BP=1 kilometer
Now PQ=PN+NQ=PN+BM
=BPsin60
0
+ABsin30
0
......... ∵sin(Θ)=
Hypotenuse
Opposite
for right ∠△
=1.
2
3
+1.
2
1
=
2
3
+1
m
The height of the mountain is
2
3
+1
m.
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