5. Functions, Transformations and Trigonometry

Applications Of Trigonometry — Quiz

Test your understanding of applications of trigonometry with 5 practice questions.

Practice Questions

Question 1

A ship is traveling at a constant speed. At 10:00 AM, the angle of elevation to a lighthouse is $30^\circ$. At 10:30 AM, the angle of elevation to the same lighthouse is $60^\circ$. If the lighthouse is 100 feet tall, what is the distance the ship traveled between 10:00 AM and 10:30 AM?

Question 2

A Ferris wheel has a radius of 40 feet and its center is 50 feet above the ground. The wheel makes one full rotation every 2 minutes. If a rider starts at the lowest point, which of the following equations models the height $h(t)$ of the rider above the ground at time $t$ (in minutes)?

Question 3

Two observers are 1000 feet apart on opposite sides of a hot air balloon. The angle of elevation from the first observer to the balloon is $60^\circ$, and from the second observer to the balloon is $45^\circ$. What is the height of the hot air balloon?

Question 4

A ship leaves port and sails 30 miles on a bearing of $045^\circ$ (Northeast). Then, it changes course and sails 40 miles on a bearing of $135^\circ$ (Southeast). What is the straight-line distance of the ship from the port?

Question 5

The depth of water at a dock can be modeled by a sinusoidal function. At 3:00 AM, the depth is at its maximum of 20 feet. At 9:00 AM, the depth is at its minimum of 10 feet. What is the equation for the depth $D(t)$ (in feet) at time $t$ (in hours after midnight)?