Question

A 10 m long flagstaff is fixed on the top of a tower on the horizontal plane. From
a point on the ground, the angles of elevation of the top and bottom of the
flagstaff are 60° and 45° respectively. Find the height of the tower.​

Answer 1

Answer:

5($\sqrt\\{3}$ + 1)

Step-by-step explanation:

Answer 2

Let the HEIGHT OF TOWER be h.

As we know that 10M LONG FLAGSTAFF is fixed on the top of a tower on the horizontal plane.

So, Total HEIGHT of the Tower including Flagstaff will be (h + 10) Metres.

Now, Let the Distance between the Base of the TOWER and POINT on ground be x.

As we got that the angle of elevation of top of the flagstaff is 60⁰.

→ tan 60⁰ = (h + 10)/x

→ √3 = (h + 10)/x

→ x = (h + 10)/√3 ...[1]

Again, the angle of elevation of bottom of the flagstaff is 45⁰.

→ tan 45⁰ = h/x

→ 1 = h/x

→ x = h ...[2]

_______

From the Second EQUATION;

→ x = (h + 10)/√3

→ h = (h + 10)/√3

→ √3h = h + 10

→ √3h - h = 10

→ h(√3 - 1) = 10

→ h = 10/(√3 - 1)

→ h = 10(√3 + 1)/(√3 - 1)(√3 + 1)

→ h = 10(√3 + 1)/2

→ H = 5(√3 + 1)

Hence, The HEIGHT OF THE TOWER is 5(√3 + 1) Metres.