The angle of elevation of the top of a tower at a point on the ground 37 m away from the foot of the tower is 45°. What is the height of the tower?

Question: The angle of elevation of the top of a tower at a point on the ground 37 m away from the foot of the tower is 45°. What is the height of the tower?

Solution:


Let AB be tower and C is a point on the ground 37 m away
From the foot of tower B
The angle of elevation is 45°

Let h be the height of the tower.
∴ tanθ = AB/BC
⇒ tan45^∘ = AB/37
⇒ 1 = AB/37
⇒ AB = 37 m