# Answer to Question #6118 in Trigonometry for Marc Sunga

Question #6118

a student stands a certain distance from a building and measures the angle to the top of the building 18.8. the student then walks 24n straight towards the build and measures the angle to the top of the building as 20.2 what is the height of the building

Expert's answer

Let h - be the height of building, d1 - first distance to the building and d2 - second distance.Student, bottom and top points of building are forming right-angled triangle where h and distance d (d1 or d2) are cathetus, using that

fact:

1) ctg 18.8 = d1 / h and d1=h*ctg 18.8

2) ctg 20.2 = d2 / h and d2=h*ctg 20.2

also is known that d1 - d2 = 24

then

h*ctg 18.8 - h*ctg 20.2 = 24,

h*(ctg 18.8 - ctg 20.2) = 24

h = 24 / (ctg 18.8 - ctg 20.2) = 24 / 0.219 = 109.59

Answer: the height of the building is 109.59 m

fact:

1) ctg 18.8 = d1 / h and d1=h*ctg 18.8

2) ctg 20.2 = d2 / h and d2=h*ctg 20.2

also is known that d1 - d2 = 24

then

h*ctg 18.8 - h*ctg 20.2 = 24,

h*(ctg 18.8 - ctg 20.2) = 24

h = 24 / (ctg 18.8 - ctg 20.2) = 24 / 0.219 = 109.59

Answer: the height of the building is 109.59 m

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