Question

sơn canh 609
(diagram: right triangle with vertical leg labeled 5, horizontal leg labeled z, angle at horizontal leg- hypotenuse vertex labeled 40°)

Explanation:

Step1: Identify the trigonometric relation

We have a right triangle with one angle \(40^\circ\), opposite side \(5\) and adjacent side \(z\). So we use the tangent function: \(\tan(\theta)=\frac{\text{opposite}}{\text{adjacent}}\)
\(\tan(40^\circ)=\frac{5}{z}\)

Step2: Solve for \(z\)

Rearrange the formula: \(z = \frac{5}{\tan(40^\circ)}\)
We know that \(\tan(40^\circ)\approx0.8391\)
So \(z=\frac{5}{0.8391}\approx5.96\)

Answer:

\(z\approx5.96\) (or depending on the required precision, if we use more accurate value of \(\tan(40^\circ)\), the result may vary slightly)