Question

1. solve for x. round to the nearest tenth. 29 12° x x =

Explanation:

Step1: Find the adjacent angle

The adjacent angle to \(12^{\circ}\) is \(90^{\circ}-12^{\circ} = 78^{\circ}\)

Step2: Use the cosine function

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

Step3: Calculate the value

We know that \(\cos(78^{\circ})\approx0.2079\)
\(x=\frac{29}{0.2079}\approx140.4\)

Answer:

\(140.4\)