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°) = [tex]\frac{\text{Opposite side}}{\text{Adjacent side}}[/tex]
= [tex]\frac{DC}{BC}[/tex]
= [tex]\frac{h}{a}[/tex]
h = a[tan(56°)] --------(1)
By applying tangent rule in ΔACD,
tan(22°) = [tex]\frac{\text{Opposite side}}{\text{Adjacent side}}[/tex]
tan(22°) = [tex]\frac{DC}{BC+AC}[/tex]
= [tex]\frac{h}{a+2400}[/tex]
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