Question

1. explain your plan of attack to find the value for x, then find x. round to one decimal place if needed.

a. plan of attack: solve for x:

Explanation:

Step1: Find \( h \) using the left - hand right - triangle

Use the sine function: \( \sin\theta=\frac{\text{opposite}}{\text{hypotenuse}} \).
For the left - hand right - triangle with \( \theta = 37^{\circ} \) and hypotenuse \( 37\) m, we have \( \sin37^{\circ}=\frac{h}{37} \), so \( h = 37\times\sin37^{\circ} \).

$$h=37\times0.6018\approx22.3$$

Step2: Find \( x \) using the right - hand right - triangle

For the right - hand right - triangle with \( \theta = 45^{\circ} \), since \( \sin45^{\circ}=\frac{h}{x} \) and \( \sin45^{\circ}=\frac{\sqrt{2}}{2}\approx0.707 \), and \( h\approx22.3 \).
We can solve for \( x \) using the formula \( x=\frac{h}{\sin45^{\circ}} \).

$$x=\frac{22.3}{0.707}\approx31.5$$

Answer:

\( x\approx31.5 \)