Trigonometry Word Problem

Question

Parasailing is an adventure sport in which a parachute and a rider are towed by a boat. The height of the parasail rider depends on both the length of the tow line and the speed of the boat. A safe speed range for the boat is 15 to 30 miles per hour. This range allows enough lift for takeoff yet maintains enough control for a smooth, sustained flight. A boat is traveling at 30 miles per hour with a tow line of 400 feet will give a parasail rider a height of 300. 

(a) The angle of elevation (rounded to the nearest integer) from the boat to the parasail rider is:

(b) The horizontal distance (rounded to the nearest hundredth) from the parasail rider to the boat is: _____ feet.

Answer 1

a) Sin^-1θ = 300/400

θ = 48.59 = 49°

Length of rope L = √(400² - 300²) = 264.58 ft.

| rider

/ |

400' / |

/ | 300' h

/ |

/ |

/ |

_Θ___________________ __ |

Boat L

Answer 2

If you draw out the triangle, let's call the angle of elevation x, the opposite side based on the x is 300 ft, and the hypotenuse is 400 ft. Let's apply SOH CAH TOA rule, we will be using SOH to find the angle of elevation.

sin x=300/400

(a)

x=sin^-1(300/400)=48.59=49 degrees

^{(b) Using Pythagorean theorem to get horizontal distance}

a²+b²=c²

a²+300²=400²

a²=70000

a=264.575=265 ft