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Question

At the foot of a mountain, the elevation of it summit is 45°; after ascending 1000 m towards the mountain up a slope of 30° inclination, the elevation is found to be 60°. Find the height of the mountain.

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Solution


Suppose, AB is a mountain of height t + x.

In DFC,sin30°=x1000 x=1000×12=500 mand tan30°=xyy=xtan30°=5003In ABC,tan45°=t+xy+zt+x=y+z ...1In ADE,tan60°=tzt=3z ...2From 1 and 2, we have 3z+x=y+zz3-1=5003-1z=500 m t=3z=5003

Hence, height of the mountain = t+x=5003+500=5003+1 m .

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