A flag post stands on the top of a building.From a point on the ground, the angles of elevation of the top and bottom of the flag post are 60∘ and 45∘ respectively. If the height of the flag post is 10m, find the height of the building. (3=1.732)

Question

A flag post stands on the top of a building.From a point on the ground, the angles of elevation of the top and bottom of the flag post are 60∘ and 45∘ respectively. If the height of the flag post is 10m, find the height of the building. (3​=1.732)

Filo · Accepted Answer

Let A be the point of observation and B be the foot of the building.Let BC denote the height of the building and CD denote height of the flag post.Given that ∠CAB=45∘,∠DAB=60∘ and CD=10mLet BC=h metres and AB=x metres.Now, in the right angled △CAB,tan45∘=ABBC​.Thus, AB=BC   i.e., x=h                    (1)Also, in the right angled △DAB,tan60∘=ABBD​⇒AB=tan60∘h+10​⇒x=3​h+10​                    (2)From (1) and (2), we get   h=3​h+10​⇒3​h−h=10 ⇒h=(3​−110​)(3​+13​+1​)=3−110(3​+1)​=5(2.732)=13.66mHence, the height of the building is 13.66m.

Question Text	A flag post stands on the top of a building.From a point on the ground, the angles of elevation of the top and bottom of the flag post are $6 0^{\circ}$ and $4 5^{\circ}$ respectively. If the height of the flag post is $10$ m, find the height of the building. $(3 = 1.732)$
Answer Type	Text solution:1
Upvotes	150

A flag post stands on the top of a building.From a point on the ground, the angles of elevation of the top and bottom of the flag post are $6 0^{\circ}$ and $4 5^{\circ}$ respectively. If the height of the flag post is $10$ m, find the height of the building. $(3 = 1.732)$

Text solutionVerified

Practice questions from similar books

A flag post stands on the top of a building.From a point on the ground, the angles of elevation of the top and bottom of the flag post are 60∘ and 45∘ respectively. If the height of the flag post is 10m, find the height of the building. (3​=1.732)

Text solutionVerified

Practice questions from similar books

A flag post stands on the top of a building.From a point on the ground, the angles of elevation of the top and bottom of the flag post are $6 0^{\circ}$ and $4 5^{\circ}$ respectively. If the height of the flag post is $10$ m, find the height of the building. $(3 = 1.732)$