Question

15 POINTS! PLEASE HELP!

Answer 1

Answer:

DC = 1332.95 feet

Step-by-step explanation:

From the figure attached,

Let the measure of DC = h ft

And measure of side BC = a ft

By applying tangent ratio in ΔBCD,

tan(56°) = $\frac{\text{Opposite side}}{\text{Adjacent side}}$

             = $\frac{DC}{BC}$

             = $\frac{h}{a}$

h = a[tan(56°)] --------(1)

By applying tangent rule in ΔACD,

tan(22°) = $\frac{\text{Opposite side}}{\text{Adjacent side}}$

tan(22°) = $\frac{DC}{BC+AC}$

             = $\frac{h}{a+2400}$

h = (a + 2400)tan(22°) ------- (2)

Equating the values of h from equations (1) and (2),

a[tan(56°)] = (a + 2400)tan(22°)

a[tan(56°) - tan(22°)] = 2400[tan(22°)]

1.0785a = 968.6629

a = 899.085 ft

From equation (1),

h = 899.085[tan(56°)]

h = 1332.948

h ≈  1332.95 ft