The angles of elevation of the top of a tower from the top and foot of a pole are respectively 30^ and 45^ . If h _ T is the height of the tower and h_p is the height of the pole, then which of the following are correct? 1. 2 ~h _ P h _ T 3+ 3 = h _ P ^2 2. h _ T - h _ P 3 +1 = h _ P 2 3. 2 ( ~h _ P + h _ T ) h _ P =4+ 3 Select the correct answer using the code given below.

Step-by-step solution

Let the distance between tower and pole be ' x '. aligned & 45^ = h _ t x h _ t x =1 & ~h _ t = x . aligned Now, 30^ = h_ t - h _ p x 1 3 = h _ t - h _ p x aligned & 1 3 = h _ t - h _ p h _ t & 1 3 -1 = h _ t - h _ p h _ t - ( h _ t - h _ p ) aligned 3 +1 2 = h _ t - h _ p h _ p h _ t - h _ p 3 +1 = h _ p 2 (1) So, statement ' 2 ' is correct. Now, h_t-h_p h_p = 3 +1 2 h_t-h_p+2 h_p h_p = 3 +1+4 2 h _ t + h _ p h _ p = 5+ 3 2 (2) So, statement ‘3’ is incorrect.