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15 POINTS! PLEASE HELP!

To measure the distance across a wide river surveyors use a technique of measuring angles to a fixed point on the other side of the river. In the diagram below, a survey starts a point A and find m

15 POINTS PLEASE HELP To Measure The Distance Across A Wide River Surveyors Use A Technique Of Measuring Angles To A Fixed Point On The Other Side Of The River class=

Sagot :

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

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