A vertical tower stands on a horizontal plane and is surmounted by a flag-staff of height 7 m. From a point on the plane, the angle of elevation of the bottom of the flag-staff is 30° and that of the top of the flag-staff is 45°. Find the height of the tower.
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Height of the tower = (√3-1)/7 m
Step-by-step explanation:
The tower and flagstaff form the perpendicular of the right-angled triangle. Flagstaff is 7m in height. Let height of the tower be x. Let AB be the perpendicular, the opposite side to angle C. Angle B is 90 degrees. AC is the hypotenuse and BC is the adjacent side.
So Tan 30 = Opposite/adjacent
1/√3 = x/BC
So BC = x√3 ----(1)
Now Tan 45 = opposite / adjacent
1 = (7 + x) / BC
Substituting BC, we get:
BC = 7 + x
x√3 = 7 + x
x = (√3-1)/7 m
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