Question

if \\(\frac{y}{x} = 0.9\\), what is the measure of \\(\alpha\\) to the nearest degree? (there are two right - angled triangles in the image, one with legs labeled \\(x\\), \\(y\\) and hypotenuse \\(z\\), and the other with leg labeled \\(y\\), angle \\(\alpha\\) and hypotenuse \\(s\\))

Explanation:

Step1: Identify trigonometric ratio

For angle $\alpha$ in the right triangle, $\frac{y}{z} = \sin\alpha = 0.9$

Step2: Calculate inverse sine

$\alpha = \arcsin(0.9)$

Step3: Compute and round to degree

Use a calculator to find $\arcsin(0.9) \approx 64^\circ$

Answer:

$64^\circ$