Question

(continued)
e. if \\(\frac{x}{z} = 0.7\\), what is the measure of \\(\alpha\\) to the nearest degree?

1. in the triangle shown, the measure of angle \\(g\\) is 45 degrees, and the length of \\(\overline{hi} = b\\) cm. what is an expression for the length of \\(\overline{hg}\\)?

Explanation:

Step1 (Question 6): Identify trigonometric ratio

For angle $\alpha$, $\frac{x}{t} = \sin\alpha = 0.7$

Step2 (Question 6): Calculate inverse sine

$\alpha = \arcsin(0.7)$

Step3 (Question 6): Round to nearest degree

$\alpha \approx 44^\circ$

Step1 (Question 7): Identify trigonometric ratio

For $\angle G=45^\circ$, $\sin(45^\circ) = \frac{HI}{HG}$

Step2 (Question 7): Substitute known values

$\sin(45^\circ) = \frac{b}{x}$, where $x=HG$

Step3 (Question 7): Solve for $HG$

$x = \frac{b}{\sin(45^\circ)} = \frac{b}{\frac{\sqrt{2}}{2}} = b\sqrt{2}$

Answer:

Question 6: $44^\circ$
Question 7: $b\sqrt{2}$ cm