Answer: b = sqrt(45)
This is equivalent to 3*sqrt(5)
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Explanation:
The smaller triangle on the left is a right triangle.
The legs of this triangle are b and 6. The hypotenuse is 9.
Use the pythagorean theorem to find b
a^2+b^2 = c^2
6^2+b^2 = 9^2
36+b^2 = 81
b^2 = 81-36 ... subtracting 36 from both sides
b^2 = 45
b = sqrt(45)
We can simplify this, but based on the answer format your teacher gave you, it appears your teacher does not want you to simplify. So we stop here.
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If you want to simplify, then,
b = sqrt(45)
b = sqrt(9*5) ...... note how one factor is a perfect square
b = sqrt(9)*sqrt(5) ..... the rule is sqrt(xy) = sqrt(x)*sqrt(y)
b = 3*sqrt(5)
