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Using the law of cosines, it is found that the distance across the lake is of 978.5 feet.
<h3>What is the law of cosines?</h3>The law of cosines states that we can find the angle C of a triangle as follows:
in which:
- c is the length of the side opposite to angle C.
- a and b are the lengths of the other sides.
In this problem, the parameters are:
a = 800, b = 900, C = 70º.
Hence the distance across the lake is c, found as follows:
c² = 800² + 900² - 2(800)(900)cos(70º)
c² = 957491
c = 978.5.
The distance across the lake is of 978.5 feet.
More can be learned about the law of cosines at brainly.com/question/2491835
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