Applying the Pythagorean theorem, the length of b, to the nearest tenth, is: 11.2.
The Pythagorean theorem is the theorem that is applied when finding any length of a right triangle. Where a and b are the smaller sides of the right triangle, and c is the longest side (hypotenuse) of the right triangle, the Pythagorean theorem states that: a² + b² = c².
We are given the following regarding a right triangle:
a = 10 (one of the smallest side)
c = 15 (the longest side/hypotenuse)
Plug in the values into a² + b² = c²:
10² + b² = 15²
100 + b² = 225
Subtract 100 from both sides
100 + b² - 100 = 225 - 100
b² = 125
Square both sides
√b² = √125
b ≈ 11.2
The length of b, to the nearest tenth, is: 11.2.
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