A bridge is being built across a canyon The length of the br

A bridge is being built across a canyon. The length of the bridge is 5025 ft. From the deepest point in the canyon, the angles of elevation of the ends of the bridge are 75 degree and 72 degree. How deep is the canyon? The canyon is ft deep.(Round to the nearest foot as needed.)

Solution

The viewer is at deepest point looking upward from 2 endpoints of the bridge(elevation), 72 + 75 =147° is the angle for the length of the bridge, dropping perperdicular line from where the viewer divides the angle @ 72° and 75°, then complement of 72° is 18° and 75° is 15°...
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let:
a plus b=c (distance of the bridge)
x and y are the legs
h is the height from deepest point
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X=15°
Y=18°
C=147°
c=5025 ft
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use sine law:
x/sine X=c/sine C
x=5025*sine 15/sine 147
x= 2387.94 ft
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a/sine A=x
a=x*sine 72
a= 2271.066 ft
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use pythagorean:
h^2=x^2-a^2
h^2=2387.94^2- 2271.066^2
h=737.9 ft
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