A flagstaff on the top of a house subtends the same angle P at two points distance a and b from the house and on the same side of it, then the length of flagstaff is.

Question

A flagstaff on the top of a house subtends the same angle P at two points distance a and b from the house and on the same side of it, then the length of flagstaff is. (A) (a + b) sin β (B) (a + b) cos β (C) (a + b) tan β (D) (a + b) cot β

Tardigrade Admin · Accepted Answer

Let PQ be the length of the flagstaff on the top P of the house OP. Let ΔQBP = β , ΔQAP = β. Let O be the centre of the circle through A, B, P, Q. Let M be the mid-point of AB and N be the midpoint of PQ. From ΔONQ, tan β = (NQ/ON) or NQ = ON tan β NQ = CM tan β Also BM = (1/2) AB = (1/2) (BA - AC) = (1/2) (b - a) QN = (CA + AM) tan β = (CA + MB) tan β = ( a + (b- a/2) ) tan β = (a +b/2) tan β ∴ PQ = 2NQ = (a + b) tan β

Q. A flagstaff on the top of a house subtends the same angle P at two points distance a and b from the house and on the same side of it, then the length of flagstaff is.

$(a + b)$ sin $β$

$(a + b)$ cos $β$

$(a + b)$ tan $β$

$(a + b)$ cot $β$

Q. A flagstaff on the top of a house subtends the same angle P at two points distance a and b from the house and on the same side of it, then the length of flagstaff is.

(a+b) sin β

(a+b) cos β

(a+b) tan β

(a+b) cot β

$(a + b)$ sin $β$

$(a + b)$ cos $β$

$(a + b)$ tan $β$

$(a + b)$ cot $β$