The angle elevation from a point A to the top of the Washington Monument is 32 degrees. From point B, which is not the same line but 55 feet closer to the monument, the angle elevation to the top is 38 degrees. Find the height of the Washington Monument.
6 answers
Is it 1.27
Angle in point A = 32 °
tan 32 ° = H / L
L = H / tan 32 ° = H * ctg 32 °
Angle in point B = 38 °
tan 38 ° = H / ( L - 55 )
L - 55 = H / tan 38 ° = H * ctg 38 °
L - 55 = H * ctg 38 ° Add 55 to both sides
L - 55 + 55 = H * ctg 38 + 55
L = H * ctg 38 ° + 55
L = L
H * ctg 32 ° = H * ctg 38 ° + 55 Subtract H * ctg 38 ° to both sides
H * ctg 32 ° - H * ctg 38 ° = H * ctg 38 ° + 55 - H * ctg 38 °
H * ctg 32 ° - H * ctg 38 ° = 55
H * ( ctg 32 ° - ctg 38 ° ) = 55 Divide both sides by ( ctg 32 ° - ctg 38 ° )
H = 55 / ( ctg 32 ° - ctg 38 ° )
H = 55 / ( 1.60033 - 1.27994 )
H = 55 / 0.32039
H = 171.666
But in w i k i p e d i a you can find that Washington Monument standing 555 feet 5 1 ⁄ 8 inches (169.294 m) tall.
Probably measuring unit is the meter, not the feet.
tan 32 ° = H / L
L = H / tan 32 ° = H * ctg 32 °
Angle in point B = 38 °
tan 38 ° = H / ( L - 55 )
L - 55 = H / tan 38 ° = H * ctg 38 °
L - 55 = H * ctg 38 ° Add 55 to both sides
L - 55 + 55 = H * ctg 38 + 55
L = H * ctg 38 ° + 55
L = L
H * ctg 32 ° = H * ctg 38 ° + 55 Subtract H * ctg 38 ° to both sides
H * ctg 32 ° - H * ctg 38 ° = H * ctg 38 ° + 55 - H * ctg 38 °
H * ctg 32 ° - H * ctg 38 ° = 55
H * ( ctg 32 ° - ctg 38 ° ) = 55 Divide both sides by ( ctg 32 ° - ctg 38 ° )
H = 55 / ( ctg 32 ° - ctg 38 ° )
H = 55 / ( 1.60033 - 1.27994 )
H = 55 / 0.32039
H = 171.666
But in w i k i p e d i a you can find that Washington Monument standing 555 feet 5 1 ⁄ 8 inches (169.294 m) tall.
Probably measuring unit is the meter, not the feet.
Remark:
ctg is cotangent ( cot )
ctg is cotangent ( cot )
I use a slightly different method.
In my sketch , I labeled the top of the monument P and the bottom Q
By properties of the sum of angles in a triangle,
in triangle ABP , angle A = 32°, angle ABP = 142, and angle APB = 6°
using the Sine Law:
BP/sin32 = 55/sin6
BP = 55sin32/sin6 = 278.8289..
now in the right-angle triangle PBQ
sin 38° = PQ/BP
PQ = 278.8289..(sin38) = 171.6642...
the monument is appr 171.7 ft heigh
In my sketch , I labeled the top of the monument P and the bottom Q
By properties of the sum of angles in a triangle,
in triangle ABP , angle A = 32°, angle ABP = 142, and angle APB = 6°
using the Sine Law:
BP/sin32 = 55/sin6
BP = 55sin32/sin6 = 278.8289..
now in the right-angle triangle PBQ
sin 38° = PQ/BP
PQ = 278.8289..(sin38) = 171.6642...
the monument is appr 171.7 ft heigh
Reiny,
Are you sure that the height of the Washington Monument is 171.7 FEET?
Are you sure that the height of the Washington Monument is 171.7 FEET?
Bosnian, thanks for catching that
The question used feet as its units, and I just did the math without really thinking about that height.
I think the linear units should have been metres and not feet.
Both of our numerical values were correct, you also had 171.7
I recall taking the elevator up back in the 60's and then walking down the stairs of the monument. Very interesting to see the huge stones from the inside with their place of origin chiseled into them
The question used feet as its units, and I just did the math without really thinking about that height.
I think the linear units should have been metres and not feet.
Both of our numerical values were correct, you also had 171.7
I recall taking the elevator up back in the 60's and then walking down the stairs of the monument. Very interesting to see the huge stones from the inside with their place of origin chiseled into them
1 answer