The length of AB is 220.6 meters
The given parameters are:
BC = 786
B = 110.2
C = 13.5
Start by calculating angle A using
A = 180 - B - C --- angles in a triangle
This gives
A = 180 - 110.2 - 13.5
Evaluate
A = 56.3
The side length AB is then calculated using:
AB/sin(C) = BC/sin(A)
Substitute known values
AB/sin(13.5) = 786/sin(56.3)
Multiply both sides by sin(13.5)
AB = sin(13.5) * 786/sin(56.3)
Evaluate
AB = 220.6
Hence, the length of AB is 220.6 meters
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The length of the AB is 220.55 meters if the distance BC of 786 m is laid off on one side of the river.
The triangle can be defined as a three-sided polygon in geometry, and it consists of three vertices and three edges. The sum of all the angles inside the triangle is 180°.
We have:
The distance AB across a river, a distance BC of 786 m is laid off on one side of the river.
Applying sine rule :
a/sinA =b/sinB = c/sinC
AB/sinC = BC/sinA
From the figure:
Angle A = 180 - 110.2 - 13.5 = 56.3 degrees
AB/sin13.5 = 786/sin56.3
AB = 786sin13.5/sin56.3
AB = 220.55 meters
Thus, the length of the AB is 220.55 meters if the distance BC of 786 m is laid off on one side of the river.
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