Question

solve for y. simplify the answer, rationalize the denominator if necessary, but do not convert your answer to decimal form. show your work here hint: to add the square root symbol (√), type
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Explanation:

Step1: Use cosine function

In a right - triangle, \(\cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}}\). Here \(\theta = 45^{\circ}\), the adjacent side is \(y\) and the hypotenuse is \(25\). So \(\cos45^{\circ}=\frac{y}{25}\).

Step2: Substitute the value of \(\cos45^{\circ}\)

Since \(\cos45^{\circ}=\frac{\sqrt{2}}{2}\), we have \(\frac{\sqrt{2}}{2}=\frac{y}{25}\).

Step3: Solve for \(y\)

Cross - multiply: \(y = 25\times\frac{\sqrt{2}}{2}=\frac{25\sqrt{2}}{2}\)

Answer:

\(y=\frac{25\sqrt{2}}{2}\)