Question

which way is the correct one to solve for b?
b=√(17²−15²)
b= cos(90)
b=sin(90)

Explanation:

The triangle is a right - triangle (since one angle is 90 degrees as it's a right - angled triangle representation). In a right - triangle, we can use the Pythagorean theorem which states that for a right - triangle with hypotenuse \(c\) and the other two sides \(a\) and \(b\), \(c^{2}=a^{2}+b^{2}\). Here, if the hypotenuse is 17 cm and one of the legs is 15 cm, and we want to find the other leg \(b\), we can re - arrange the Pythagorean theorem as \(b = \sqrt{c^{2}-a^{2}}\). Substituting \(c = 17\) and \(a = 15\), we get \(b=\sqrt{17^{2}-15^{2}}\).

The other two options \(b = \cos(90)\) and \(b=\sin(90)\) are incorrect because \(\cos(90^{\circ})=0\) and \(\sin(90^{\circ}) = 1\), and these are values of trigonometric functions at 90 degrees, not related to finding the side length of a right - triangle in this context.

Answer:

The correct way to solve for \(b\) is \(b=\sqrt{17^{2}-15^{2}}\) (the option in the orange box).