Geometry. find the indicated side of the triangle. include a clear answer and description if possible.

Hello!

To find side b of this right triangle, you would need to use cosine.

The formula for cosine is opposite / hypotenuse.

Since this is a 45-45-90 triangle, this type of triangle has unique characteristics compared to other triangles.

The ratio between the angles 45-45-90 are 1:1:√2. (or x : x : x√2).

45 → x, 90 → x√2

The given ratio says that the other sides of the triangle should be equal to half the hypotenuse times the √2.

. 5√2 is equal to about 7.071678...

We can check this method by using cosine.

cos(45) = b / 10 (multiply both sides by 10)

10cos(45) = b

b = 7.071678...

Therefore, the measure of side b is equal to 5√2.

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step-by-step explanation:

no, her answer is not correct.   we square the lengths of all sides and then determine whether the pythagorean theorem holds here:

9² + 15² = 306.   this is not equal to the square of the longest side ( that square being 395.   answer c is correct.