Q. 124.3( 207 Votes )
From the top of a 7 m high building, the angle of elevation of the top of a cable tower is 60° and the angle of depression of its foot is 45°. Determine the height of the tower.
Let us take AB as a building, with AB = 7 m
and CE as a cable tower
Angle of elevation from top of tree to top of cable tower∠EAD = 60°,
and angle of depression from the top of the building to the bottom of the tower is, ∠CAD = 45°
∠CAD = ∠ACB [Alternate angles]
AB = DC and EC = ED + DC ?
In Δ ABC:
where p = perpendicular and b = base, therefore
AB = BC = 7 m
In Δ EDA,
The height of tower can be calculated as:
EC = ED + DC
= 7√3 + 7
= 7(√3 +1) m
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PREVIOUSA TV tower stands vertically on a bank of a canal. From a point on the other bank directly opposite the tower, the angle of elevation of the top of the tower is 60°. From another point 20 m away from this point on the line joining this point to the foot of the tower, the angle of elevation of the top of the tower is 30° (see Fig. 9.12). Find the height of the tower and the width of the canal NEXTAs observed from the top of a 75 m high lighthouse from the sea-level, the angles of depression of two ships are 30° and 45°. If one ship is exactly behind the other on the same side of the lighthouse, find the distance between the two ships
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