Question

If the shadow of a building increases by 10 meters when the angle of elevation of the sun rays decreases from 70° to 60°, what is the height of the building?​

Answer 1

Answer:

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

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