Aflagpole 94.9 ft tall is on the top of a building. from a point on level ground, the angle of elevation of the top of the flagpole is 35.3degrees, while the angle of elevation of the bottom of the flagpole is 26.2degrees. find the height of the building.

214 ft

Step-by-step explanation:

Height of building = 94.9 ft

The angle of elevation of the top of the flagpole = θ₁ = 35.3°

The angle of elevation of the bottom of the flagpole = θ₂ = 26.2°

Let,

Height of building = x

Distance from observation point to base of building = y

I have used the exact values from the calculator.

∴ Height of the building is 214.84 ft

the sum of all the angles in a triangle are equal to 180

so you can add   the 3 given angles together to equal 180:

5y + 2y + 2y = 180

or since all three angles have the same letter, combine the 3 angles to equal 180:

9y = 180