Q52 of 68 Page 9

From the top and bottom of a building of height h, the angles of elevation of the top of a tower are α and β respectively. Prove that the height of the tower is .


Let AB be the tower and CD be the building.


We draw CE AB.


According to the question,


CD = h = BE


Let AB =y


Then, AE = AB — BE =y— h


Let CE =x. Then DB =x


In right ACE, we have




…(i)


Also, In right ABD,




…(ii)


From eq. (i) and (ii), we have








Hence, the height of the tower =


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