Answer
1158 ft
Work Step by Step
Step 1. Let $h$ represent the height of the building, and Let point P be the bottom of the building.
Step 2. From the definition of tangent function we have $\frac{h}{AP}=tan24.1^{\circ}\approx0.447$, thus $AP=h/0.447=2.236h$
Step 3. Similarly, $\frac{h}{BP}=tan30.2^{\circ}\approx0.582$, thus $BP=h/0.582=1.718h$
Step 4 Since $AB=600ft$, we have $AB=AP-BP=2.236h-1.718h=0.518h=600$ which gives $h\approx1158ft$
