A 13 ft flag pole is mounted on top of a school building. If the top of the flagpole forms a 58° angle with the ground 50 ft from the base of the building, about how tall is the school building?

Answer 1

We can build a right triangle, and use the tangent function to find the height of the school building.

We will call the height of the building, x. The total height of our triangle is the height of the building plus the height of the flagpole. So, one leg of the triangle is 13+x. The other leg, along the ground is given as 50ft. We also know the angle formed by the hypotenuse and the ground leg is 58°.

Using this angle of 58°, our opposite leg is 13+x, and our adjacent leg is 50ft. So we can use tangent function to make an equation and solve for x.

tan θ = Opp/Adj

tan (58°) = (13+x)/50

(50)tan(58°)= 13+x

((50)tan (58°) -13 = x

x ≈ 67

The building is about 67ft high

Answer 2

Let x = height of the building:

Tan 58 = (x+13)/50

x = 50(Tan 58) - 13