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 the height \( h \)

Use the sine function in the left - hand right - triangle. \(\sin37^{\circ}=\frac{h}{37}\), so \(h = 37\sin37^{\circ}\).

Step2: Find \( x \)

In the right - hand right - triangle, since \(\sin45^{\circ}=\frac{h}{x}\) and \(h = 37\sin37^{\circ}\), then \(x=\frac{37\sin37^{\circ}}{\sin45^{\circ}}\).

Calculate \(37\sin37^{\circ}\approx37\times0.6018 = 22.2666\), and \(\sin45^{\circ}=\frac{\sqrt{2}}{2}\approx0.7071\).

So \(x=\frac{22.2666}{0.7071}\approx31.5\)

Answer:

\(x\approx31.5\)