Anonymous
Anonymous asked in Science & MathematicsMathematics · 1 month ago

# 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?

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• Philip
Lv 6
1 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.

• David
Lv 7
1 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 H
Lv 7
1 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

• 1 month ago

Refer to the figure below:

In the smaller right triangle:

tan33° = h/x

x = h/tan33° ...... [1]

In the larger right triangle:

tan25° = h/(x + 407)

x + 407 = h/tan25ᵖ

x = (h/tan25ᵖ) - 407 …… [2]

[1] = [2]:

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