Question

1. A boat is 18 ft away from a point perpendicular to the shoreline. A person stands at a point down the shoreline so that a 68° angle is formed between the closest point to the boat, the person, and the boat. How far is the person from the boat? Round your answer to the nearest tenth of a foot. Show your work please to help me understand

Answer 1

Answer:

19.4 feet

Step-by-step explanation:

When calculating distances using perpendicular angles, we use trig functions such as Sin, Cos, and Tan.

• Sine is defined in a perpendicular triangle as the ratio of the opposite side to the angle over the hypotenuse.
• Cosine is defined in a perpendicular triangle as the ratio of the adjacent side to the angle over the hypotenuse.
• Tangent is defined in a perpendicular triangle as the ratio of the opposite side over the adjacent side.

Because our angle and know side value are across from each other and we need to know the hypotenuse, we chose to use Sine.

We set up the equation $sin (68) = \frac{18}{h}$.

We isolate h by multiplying h across the equal sign and dividing sin (68) across as well. $sin (68) = \frac{18}{h}\\hsin (68) = \frac{18}{h}*h\\hsin (68) = 18\\\frac{hsin (68)}{sin (68)} =\frac{18}{sin (68)}$

And finally we have $h=\frac{18}{sin (68)}$. We input to calculator.

$h=\frac{18}{0.92718} \\h=19.4 feet$

See the attached picture below showing the shore with the boat out at sea and the position of the person.