Answer:
building: 51.4 ft
flagpole: 5.3 ft
Step-by-step explanation:
The relevant trig relation is ...
Tan = Opposite/Adjacent
If we let b and p represent the heights of the building and flagpole, respectively, then we can write two equations using the tangent relation:
tan(79°) = b/10
tan(80°) = (b +p)/10
Multiplying these equations by 10 gives the values we're interested in.
b = 10·tan(79°) ≈ 51.4 . . . feet
b +p = 10·tan(80°) ≈ 56.7 . . . feet
Then the height of the flagpole is ...
p = (b+p) -b = (56.7 ft) -(51.4 ft) = 5.3 ft
The building is 51.4 ft tall.
The flagpole is 5.3 ft tall.
