A man standing 20 m from a tower estimates the angle of elavation of the top and bottom of a flagpole on the tower as 58 degrees and 55 degrees. Calculate the height of the flagpole.
How would I go about finding the height of the flagpole?
Calculate the height of the bottom:
tan55= hb/20 solve for hb
Calculate the height for the top
tan 58=ht/20 calculte ht
The difference between ht and hb is the height of the flagpole.
Thank You
To calculate the height of the flagpole, you can follow these steps:
1. Calculate the height of the bottom of the flagpole (hb):
Use the tangent function, which relates the angle of elevation (55 degrees) to the height (hb) and the distance from the tower (20 m):
tan(55) = hb / 20
Rearrange the equation to solve for hb:
hb = 20 * tan(55)
2. Calculate the height of the top of the flagpole (ht):
Use the tangent function again, this time with the angle of elevation at the top (58 degrees) and the same distance from the tower (20 m):
tan(58) = ht / 20
Rearrange the equation to solve for ht:
ht = 20 * tan(58)
3. Calculate the height of the flagpole:
The difference between the height at the top and the height at the bottom gives us the height of the flagpole:
flagpole height = ht - hb
So, by plugging the values into these equations, you can find the height of the flagpole.