2 years ago

Find two consecutive whole numbers that square root 86 lies between.

Mathematics

2 answers:

melisa1 [442]2 years ago

7 0

Find two consecutive whole numbers that square root 86 lies between.

Alexus [3.1K]2 years ago

3 0

The square root of 86 is 9.2...... Hence, it lies between 9 and 10.

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Work Shown:

$c^2 = a^2 + b^2 - 2*a*b*\cos(C)\\\\10^2 = 5^2 + 6^2 - 2*5*6*\cos(x)\\\\100 = 25 + 36 - 60*\cos(x)\\\\100 = 61 - 60*\cos(x)\\\\100 - 61 = - 60*\cos(x)\\\\39 = - 60*\cos(x)\\\\\cos(x) = \frac{39}{-60}\\\\\cos(x) = -0.65\\\\x = \arccos(-0.65)\\\\x \approx 130.5416\\\\x \approx 130.5\\\\$