The shadow of a building increased by 10 meters when the angle of elevation of the sun decreased by 10 degrees from 70 degrees to 60 degrees.
Calculate the height of the building.
I tried to construct a diagram, but was unable to make one which had both the angles of elevation and height of the building. How would I go about doing this?
Let $h$ be the height of the building and $L$ the length of the shadow. Then, we have
$$h=L\tan 60,\>\>\>\>\>h=L'\tan70$$
and
$$\frac{h}{\tan60}-\frac{h}{\tan70} = L - L' = 10$$
Thus, the height of the building is given by,
$$h = \frac{10}{\frac{1}{\tan60}-\frac{1}{\tan70}}$$