A horizontal park is in the shape of a triangle O A B with A B = 16 . A vertical lamp post O P is erected at the point O such that ∠ P A O = ∠ P B O = 15 ° and ∠ P C O = 45 ° , where C is the midpoint of A B . Then O P 2 is equal to

Step-by-step solution

Given, a horizontal park is in the shape of a triangle O A B with A B = 16 . A vertical lamp post O P is erected at the point O such that ∠ P A O = ∠ P B O = 15 ° and ∠ P C O = 45 ° , where C is the midpoint of A B . Then O P 2 is equal to Now plotting the graph of given value we get, Now in △ P A O given ∠ P A O = 15 ° So, O P O A = tan 15 ° ⇒ O A = O P cot 15 ° And in △ P C O given ∠ P C O = 45 ° So, O P O C = tan 45 ° ⇒ O P