Two buildings are facing each other on a road of width 12 metre.

Solution

Let’s denote the height of the second building as “h”. We can draw a right-angled triangle, where the first building is at the base of the triangle, the second building is at the opposite side of the triangle, and the line of sight from the top of the first building to the top of the second building is the hypotenuse of the triangle. The width of the road is the adjacent side of the triangle.

From the triangle, we can see that:

tan(60°) = h/(12 + 10)

tan(60°) is equal to √3, so we can simplify the equation to:

√3 = h/22

Multiplying both sides by 22, we get:

h√3 = 22

Dividing both sides by √3, we get:

h = 22/√3

Rationalizing the denominator by multiplying both sides by √3/√3, we get:

h = 22√3/3

Simplifying the right-hand side, we get:

h ≈ 12.72 meters

Therefore, the height of the second building is approximately 12.72 meters.