From a window h metersh metersh meters high above the ground in a street, the angles of elevation and depression of the top and foot of the other house on the opposite side of the street are ααα and βββ respectively. Show that the height of the opposite house is h(1+tanα cotβ) metersh(1+tanα cotβ) metersh(1+tanα cotβ) meters.


Answer:


Step by Step Explanation:
  1. Let WWW be the window and ABABAB be the house on the opposite side with height (h+h) meters.

    The figure below shows the given situation.
    W P A B C h' h α β h' cot α h cot β h + h'
  2. In the right-angled triangle AWP, we have cotα=WPAPcotα=WPhWP=hcotα(i)
  3. In right-angled triangle WPB, we have cotβ=WPBPcotβ=WPhWP=hcotβ(ii)
  4. On comparing eq (i) and eq (ii), we get hcotα=hcotβh=hcotβcotα=htanαcotβ
  5. Thus, height of the house = h+h=h+htanαcotβ=h(1+tanαcotβ) meters.

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