Question

solve for z. simplify the answer, rationalize the denominator if necessary, but do not convert your answer to decimal form. draw 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 \(x\), and the hypotenuse is \(28\). So \(\cos45^{\circ}=\frac{x}{28}\).
Since \(\cos45^{\circ}=\frac{\sqrt{2}}{2}\), we have \(\frac{\sqrt{2}}{2}=\frac{x}{28}\).

Step2: Solve for \(x\)

Cross - multiply: \(x = 28\times\frac{\sqrt{2}}{2}\).
Simplify the expression: \(x = 14\sqrt{2}\).

Answer:

\(14\sqrt{2}\)