Question

a mine shaft is 300 meters deep and forms an angle of depression of 65 degrees. How long is the mine shaft?

Answer 1

Answer: 331.01 meters.

Step-by-step explanation:

1. You can draw a right triangle as the one shown in the figure attached, where the lenght of the mine shaft is represented with x.

2. Therefore, you can find the  lenght of the mine shaft as following:

$sin(\alpha)=\frac{opposite}{hypotenuse}$

Where:

$\alpha=65\°\\opposite=300\\hypotenuse=x$

2. Now, you must substitute values and solve for x. Then, you obtain the following result:

$sin(65\°)=\frac{300}{x}\\x=\frac{300}{sin(65\°)}\\x=331.01$

Answer 2

See the attached picture: