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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?

Quanto
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danielmason
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1 Answers1

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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,

$$h = \frac{10}{\frac{1}{\tan60}-\frac{1}{\tan70}}$$

Quanto
  • 97,352
  • Thanks a lot. How did you get 10/(1/sin60 etc)? I got h = 10 * (sin70*sin60)/(sin70-sin60), how would I change that into the form you have written? – danielmason Oct 16 '19 at 04:08