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The angle of elevation of the top of a v...

The angle of elevation of the top of a vertical tower a point on the ground is `60^(@)` From another point 10 m vertical above the first, its angle of elevation is `45^(@)`. Find the height of the tower.

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let AB be a vertical tower, From point C, the angle of elevation of the top of tower is `60^(@)` and from points D as shown, the angle of elevation of the tower is `45^(@)`
`:.angleACB=60^(@), angleADE=45^(@)" and "DC=10m`
In `DeltaADE`,
`tan45^(@)=(AE)/(DE)rArrAE=DE...(1) ( :' tan45^(@)=1)`
In `DeltaABC`,
`tan60^(@)=(AB)/(BC)rArrsqrt3=(AB)/(DE) ( :' BC=DE)`
`rArr AB=sqrt3DE`
`rArr AE+BE=sqrt3AE [from(1)]`
`rArrBE=AE(sqrt3-1)`
`rArrAE=(BE)/(sqrt3-1)=10/(sqrt3-1)xx(sqrt3+1)/(sqrt3+1)`
`=(10(1.732+1))/(3-1)=5xx2.732=13.66`
Now, `AB=AE+BE=AE+CD=(23.66+10)m=13.66m`
`:. " Height of the tower "=23.66 m`
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