Question

solve for z. do not convert your answer to decimal form. rationalize the denominator and simplify your answer if necessary.
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, \(\theta = 30^{\circ}\), the adjacent side is \(z\), and the hypotenuse is \(26\). So, \(\cos30^{\circ}=\frac{z}{26}\).

Step2: Substitute the value of \(\cos30^{\circ}\)

We know that \(\cos30^{\circ}=\frac{\sqrt{3}}{2}\). Then \(\frac{\sqrt{3}}{2}=\frac{z}{26}\).

Step3: Solve for \(z\)

Cross - multiply: \(z = 26\times\frac{\sqrt{3}}{2}\). Simplify the fraction: \(z = 13\sqrt{3}\).

Answer:

\(z = 13\sqrt{3}\)