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.

Guest Feb 9, 2021

#1**0 **

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 !

Guest Feb 9, 2021