Question

for z. simplify the answer, rationalize the denominator if necessary, brt your answer to decimal form. draw 45° 27 z ur work here dd 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 \(z\), and the hypotenuse is \(27\). So \(\cos45^{\circ}=\frac{z}{27}\).

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

Since \(\cos45^{\circ}=\frac{\sqrt{2}}{2}\), we have \(\frac{\sqrt{2}}{2}=\frac{z}{27}\).

Step3: Solve for \(z\)

Cross - multiply: \(z = 27\times\frac{\sqrt{2}}{2}\).

Step4: Calculate the decimal value

\(\sqrt{2}\approx1.414\), then \(z=\frac{27\times1.414}{2}=\frac{38.178}{2}=19.089\).

Answer:

\(z=\frac{27\sqrt{2}}{2}\approx19.09\)