Question

Marcus para sailing in Florida. The angle of depression from his line of sight to the boat is 41 °. if the cable attaching Mark to the boat is 500 ft long how many feet is Mark above the water

Answer 1

As you can see, a right triangle is formed in the situation that the statement describes. So to solve the exercise you can use the trigonometric ratio sin(θ):

$\sin (\theta)=\frac{\text{opposite side}}{\text{hypotenuse}}$

Graphically

So, in this case, you have

$\begin{gathered} \theta=41\text{\degree} \\ \text{Opposite side = Mark's height above water } \\ \text{Hypotenuse = 500 ft} \\ \sin (\theta)=\frac{\text{opposite side}}{\text{hypotenuse}} \\ \sin (41\text{\degree})=\frac{\text{Mark's height above water }}{500ft} \\ \text{Multiply by 500ft from both sides of the equation} \\ \sin (41\text{\degree})\cdot500ft=\frac{\text{Mark's height above water }}{500ft}\cdot500ft \\ \sin (41\text{\degree})\cdot500ft=\text{Mark's height above water } \\ 328.03ft=\text{Mark's height above water } \end{gathered}$

Therefore, Mark is 328.03 feet above the water.