A scuba diver is at the surface of the water and preparing to swim to a shipwreck. The shipwreck is 20 meters underwater and the diver is 65 meters away from a buoy that shows where the shipwreck lies. At what angle does the diver have to swim to reach the shipwreck to the nearest tenth of a degree?
draw it, it always helps
you will see that you need to use Tangent
"Opposite over adjacent"
tan(angle)=65/20
To determine the angle at which the diver needs to swim to reach the shipwreck, we can use trigonometry. Specifically, we can use the tangent function, which is defined as the ratio of the opposite side to the adjacent side in a right triangle.
Let's define the variables:
- Opposite side (O): the depth of the water, which is 20 meters
- Adjacent side (A): the horizontal distance from the buoy to the shipwreck, which is 65 meters
Now, we can use the tangent function:
tan(angle) = O / A
Substituting in the known values:
tan(angle) = 20 / 65
To find the angle, we need to take the inverse tangent (also known as arc-tangent or atan) of both sides:
angle = atan(20 / 65)
Calculating this using a calculator or software, we find that the angle is approximately 17.2 degrees to the nearest tenth of a degree. So, the diver needs to swim at an angle of about 17.2 degrees to reach the shipwreck.