Question

1. select the correct equation to solve for missing side d. image of a ship with a right triangle formed, hypotenuse 30 m, angle 39 degrees, side d opposite? or adjacent? options: \\(\cos 39 = \frac{d}{30}\\), \\(\cos d = \frac{30}{30}\\) (maybe typo), \\(\sin 39 = \frac{d}{30}\\), \\(\sin 39 = \frac{30}{d}\\) (partial ocr for last option)

Explanation:

Step1: Recall SOHCAHTOA

In a right triangle, \(\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}\), \(\cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}}\), \(\tan\theta=\frac{\text{opposite}}{\text{adjacent}}\).

Step2: Identify sides

Here, \(\theta = 39^\circ\), hypotenuse \(= 30\) m, opposite side to \(39^\circ\) is \(d\).

Step3: Apply sine formula

Using \(\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}\), substitute \(\theta = 39^\circ\), opposite \(= d\), hypotenuse \(= 30\). So \(\sin39^\circ=\frac{d}{30}\).

Answer:

\(\sin 39^\circ=\frac{d}{30}\) (the third option, assuming the options are ordered as given with the third being \(\sin 39=\frac{d}{30}\))