Asked by Allison
If the shadow of a building increases by 10 meters when the angle of elevation of the sun rays decreases from 70o to 60o, what is the height of the building?
Answers
Answered by
Reiny
Make two right-angled triangles,
let the base (length of shadow) of the first be x, and its base angle is 70°
let the base of the second be x+10, and label its base angle as 60°
For both let the height (the building) be h
from the first:
tan70 = h/x ---> h = xtan70
from the second:
tan60 = h/(x+10) ---> h = (x+10)tan60
then xtan70 = (x+10)tan60
xtan70 = xtan60 + 10tan60
xtan70 - xtan60 = 10tan60
x(tan70-tan60) = 10tan60
x = 10tan60/(tan70-tan60)
back in h = xtan70
h = 10tan60tan70/(tan70-tan60)
= appr 46.9 m
let the base (length of shadow) of the first be x, and its base angle is 70°
let the base of the second be x+10, and label its base angle as 60°
For both let the height (the building) be h
from the first:
tan70 = h/x ---> h = xtan70
from the second:
tan60 = h/(x+10) ---> h = (x+10)tan60
then xtan70 = (x+10)tan60
xtan70 = xtan60 + 10tan60
xtan70 - xtan60 = 10tan60
x(tan70-tan60) = 10tan60
x = 10tan60/(tan70-tan60)
back in h = xtan70
h = 10tan60tan70/(tan70-tan60)
= appr 46.9 m
Answered by
Brisen
i im a maek a wish child, nd i hve bin working on dis problim 4 too dayz
Answered by
Anonymous
987
Answered by
imheretohelp
You need to work on both triangles that you have created, seeing as there are two unknowns. Then you have to write one equation as a function of another and plug that in. After this, it's just basic problem-solving.
The answer (rounded) = 46.86
But you may get a different answer, depending on whether you calculate the tangents at the beginning or end on the exercise.
The answer (rounded) = 46.86
But you may get a different answer, depending on whether you calculate the tangents at the beginning or end on the exercise.
Answered by
Babara
4.3432