Using the law of cosines, it is found that the distance across the lake is of 978.5 feet.
What is the law of cosines?
The law of cosines states that we can find the angle C of a triangle as follows:
[tex]c^2 = a^2 + b^2 - 2ab\cos{C}[/tex]
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:
[tex]c^2 = a^2 + b^2 - 2ab\cos{C}[/tex]
c² = 800² + 900² - 2(800)(900)cos(70º)
c² = 957491
[tex]c = \sqrt{957491}[/tex]
c = 978.5.
The distance across the lake is of 978.5 feet.
More can be learned about the law of cosines at https://brainly.com/question/2491835
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