Help, elevation question?
A woman standing at point A looks up at the top of a building and finds the angle of elevation is 33∘. She walks 407 feet away from the building to point D and finds the angle of elevation to the top of the building is now 25∘.
What is the height of the building h=___feet?
- PhilipLv 61 month ago
Put horizontal distance from base of building = d ft. & building height = h ft.;
h/d = tan33, ie., h = dtan33...(1).;
h/(d+407) = tan25, ie., h = (d+407)tan25...(2).;
By (1) & (2), dtan(33) = (d+407)tan25, ie., d(tan33-tan25) = 407tan25, ie, d =;
((407tan25)/(tan33-tan25)) ft = 1036.522579 ft and (1) now gives h = ;
1036.522579tan33 ft = 673.1256333 ft = 673 ft rounded off to nearest ft.
- DavidLv 71 month ago
Draw a sketch of two interlinked right angle triangles and by using the 'sine rules' the height of the building works out as 673.1256332 feet or about 673 feet
- Ian HLv 71 month ago
h/tan 25 = x + 407
h/tan 33 = x
h [1/tan 25 - 1/tan33)] = 407
h ~ 407/0.6046 ~ 673.1 feet
- micatkieLv 71 month ago
Refer to the figure below:
In the smaller right triangle:
tan33° = h/x
x = h/tan33° ...... 
In the larger right triangle:
tan25° = h/(x + 407)
x + 407 = h/tan25ᵖ
x = (h/tan25ᵖ) - 407 …… 
 = :
h/tan33° = (h/tan25ᵖ) - 407
(h/tan25ᵖ) - (h/tan33°) = 407
h [(1/tan25ᵖ) - (1/tan33°)] = 407
h = 407 / [(1/tan25ᵖ) - (1/tan33°)] ft
h = 673 ft
The height of the building, h = 673 feet
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- ted sLv 71 month ago
you must be missing something as you state that at 407 from the building the angle is 25° ===> h = 407 tan 25°...want to update the query ?