SOLUTION: To determine the distance between two points on opposite sides of a pond, a surveyor locates two stakes at either end of the pond and uses instrumentation to place a third stake so
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Question 631411: To determine the distance between two points on opposite sides of a pond, a surveyor locates two stakes at either end of the pond and uses instrumentation to place a third stake so that the distance across the pond is the length of a hypotenuse. If the third stake is 90m from one stake and 70 m from the other, how wide is the pond?
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
see the diagram shown here.
words are below it.
the circle is your pond.
the line marked y is the hypotenuse of the triangle formed by the lines that are 90 and 70 meters.
since tan(x) = opposite / adjacent, this means that:
tan(x) = 70/90 which means that:
x = tan^-1(70/90) which makes x = 37.87498365 degrees.
now that you know the measure of angle x, you can use the sine function to find y.
sin(x) = opposite / hypotenuse
x = 37.87... and opposite = 70 and hypotenuse = y so the equation becomes:
sin(37.87...) = 70 / y
solve for y to get:
y = 70 / sin(37.87...)
this results in y = 114.0175425 which can be rounded to 114.02 meters.
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