Find the height of the tower (XY) given the following:To find the height of a tower(XY), measurements were taken from a baseline AB. It was found that AB = 50m. angle XAY = 42.6 degrees, angle...

Find the height of the tower (XY) given the following:

To find the height of a tower(XY), measurements were taken from a baseline AB. It was found that AB = 50m. angle XAY = 42.6 degrees, angle XAB = 60 degrees, and angle ABX = 81.65 degrees.

Asked on by islnds

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justaguide's profile pic

justaguide | College Teacher | (Level 2) Distinguished Educator

Posted on

The problem given is one that involves measurements made in all the three dimensions and this should be kept in mind while solving the problem.

The tower is a vertical line with the base being X and Y being the topmost point. The line AB is a horizontal line. It is given that the angle of elevation of the line from the point A to the point Y is 42.6 degrees. The height of the tower can be determined if the distance of the point A from the point X is known. This is determined using the length of the line AB and the measure of angle XAB = 60 degrees and ABX = 81.65 degrees. The measure of angle AXB = 180 - 60 - 81.65 = 38.35. As AB = 50 m, use the law of sines to determine the length AX.

 `(AX)/(sin 81.65) = (50)/(sin 38.35)`

=> `AX ~~ 79.73`m

The height of the tower is equal to h where `h/79.73 = tan 42.6`

=> `h ~~ 73.31` m

The height of the tower is 73.31 m

Top Answer

ntretheway's profile pic

ntretheway | (Level 2) Adjunct Educator

Posted on

XY is the height of the tower (use X as the base)

AB is a 50 m baseline, some distance away from the tower.

Angle XAY = 42.6 (which is the vertical angle from ground level to the top of the tower)

Angle XAB = 60 (and is the horizontal angle between the line segment AX and AB

Angle ABX = 81.65 (the horizontal angle between the line segment AB and BX.

Find Angle AXB = 180 degrees - 60 degrees - 81.65 degrees = 38.35 degrees

Use law of sines to find distance AX:

sin 38.35/50 = sin 81.65 / AX and AX = 79.7 m

Use AX and the vertical angle to find the height of the tower:

42.6 degrees is the vertical angle between line AX and XY

Therefore,

Tan 42.6 = XY/79.7

 XY, the height of the tower is 73.3 m  Answer

 

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