the angle of elevation from the top of the tower from a distance 50m from its foot is 30degrees then find height of the tower

Question

i am not getting exact triangle

Answer 1

There are a few ways to solve this problem.  One of the ways is by using the trig functions (sin, cos, or tan).  This is the first method that I will show:

 

Using 30 degrees as our reference, since we are interested in the opposite side of the triangle (aka, the height of the tower) and we know the adjacent side of the triangle (50m), we can use:

 

tan(angle)=opposite/adjacent

 

or in our case

 

tan(30)=x/50

 

where x represents the height of the tower and 50 represents the adjacent side (or ground distance to the tower)

Multiplying both sides by 50 gives:

 

50tan(30 degrees) = x

50 tan(30 degrees) = 28.8675135 

 

So the height of the tower is 28.87 meters

 

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Alternative method using 30-60-90 triangle properties.

 

Every 30-60-90 triangle has side lengths in the ratio of 1-sqrt(3)-2

 

So to figure out the smallest side length corresponding with 30 degrees, we should divide the second length, 50m, by square root of 3

 

50/sqrt(3) = 28.8675135

 

Which gives the same answer in fewer steps, but this method can sometimes be a little difficult to understand at first.

 

Hope this helps!

Answer 2

The height, h of the tower can be found by using the relationship between the tangent and the adjacent and opposite sides of a right triangle tan(θ)=opp/adj

 

tan(30)=h/50 so h=50tan (30)=50/√3=28.867m

 

Jim