Question

1. what is α? degrees 2) what is x? feet 3) what is z? hint do not use the side that has been rounded. feet

Explanation:

Step1: Find angle \( \alpha \)

In a right - triangle, the sum of the two non - right angles is \( 90^{\circ} \).
If one non - right angle is \( 53^{\circ} \), then \( \alpha=90^{\circ}-53^{\circ} \).

Step2: Find side \( x \)

We know that \( \tan\alpha=\frac{\text{opposite}}{\text{adjacent}} \). Since \( \alpha = 37^{\circ} \) and the adjacent side to \( \alpha \) is \( 7\) ft. \( \tan\alpha=\tan37^{\circ}\approx0.75 \), and \( \tan\alpha=\frac{x}{7} \). So \( x = 7\times\tan37^{\circ}\approx7\times0.75 = 5.25\) ft.

Step3: Find side \( z \)

We know that \( \cos\alpha=\frac{\text{adjacent}}{\text{hypotenuse}} \). The adjacent side to \( \alpha \) is \( 7\) ft. \( \cos\alpha=\cos37^{\circ}\approx0.8 \), and \( \cos\alpha=\frac{7}{z} \). Then \( z=\frac{7}{\cos37^{\circ}}\approx\frac{7}{0.8}=8.75\) ft.

Answer:

1. \( 37\) degrees
2. \( 5.25\) feet
3. \( 8.75\) feet