Question

1. solve for z. round to the nearest tenth. 29 x x =

Explanation:

Step1: Find the angle of the right - angled triangle

Since the angle adjacent to \(x\) is \(12^{\circ}\), the angle inside the right - angled triangle is \(90^{\circ}-12^{\circ} = 78^{\circ}\).

Step2: Use the cosine function

In a right - angled triangle, \(\cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}}\). Here, \(\theta = 78^{\circ}\), the adjacent side is \(29\), and the hypotenuse is \(x\). So, \(\cos78^{\circ}=\frac{29}{x}\).

Step3: Solve for \(x\)

We can rewrite the equation as \(x=\frac{29}{\cos78^{\circ}}\).
We know that \(\cos78^{\circ}\approx0.2079\). Then \(x=\frac{29}{0.2079}\approx140.4\).

Answer:

\(140.4\)