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There are 2 temples, one on each bank of the river, just opposite to each other. One of the temples A is \(40 \text{ m}\) high. As observed from the top of this temple A, the angle of depression of the top and the foot of the other temple B are \(12^\circ 30'\) and \(21^\circ 48'\) respectively. Find the height of the temple B in meters.

 Feb 9, 2021
 #1
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Use the angle of dec to the base of B to find the distance to B

 

tan 21.8 = 40/x        x = 100.00713 meters           (note the 21 degrees 48 min   is    21.8 decimal degrees)

 

Now use the angle of dec to the top

tan 12.5 = 40/x          x = 180.4283  meters     this is the distance line to the  to the triangle vertex which the top intercepts

    but the top is only    100.00713  meters away

 

(180.428-100.00713)/ 180.428   * 40 = 17.829  meters high = temple B

 

 

Check  tan 12.5 = 17.829/80.428 ....check !

 Feb 9, 2021
 #2
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sketch:

 

Guest Feb 9, 2021
 #3
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Sorry....   mislabeled those two angles in the diagram....

     switch them....

Guest Feb 9, 2021

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