In these word problems and applications of trigonometry, you'll use the knowledge of the previous lectures: The SOHCAHTOA, The Law of Sines, The Law of Cosines, and Heron's Formula. Remember that the SOHCAHTOA is used in right triangles only, while the other rules can be used in any triangle. In this lecture, you'll learn how to find the height of a telephone pole if you are given the length of its shadow and the angle that the sun's rays make with the ground. In other examples, you'll work with bridge length, roads to a town and some other real life situations.
A telephone pole casts a shadow 20 feet long. If the sun's rays make a 60°
angle with the ground, how tall is the pole?
Civil engineers are planning to build a bridge across a lake, but they can't measure the width of the lake directly. They measure from a point on land that is 280 feet from one end of the planned bridge and 160 feet from the other. If the angle between these two lines measures 80°
, then how long will the bridge be?
A farmer measures the fences along the edges of a triangular field as 160 feet, 240 feet, and 300 feet. What is the area of the field?
A child is flying a kite on 200 feet of string. If the kite string makes an 40°
angle with the ground, how high is the kite?
Two straight roads lead from different points along the coast to an inland town. Surveyors working on the coast measure that the roads are 12 miles apart and make angles of 40°
with the coast. How far is it to the town along each of the roads?
Word Problems and Applications of Trigonometry
Lecture Slides are screen-captured images of important points in the lecture. Students can download and print out these lecture slide images to do practice problems as well as take notes while watching the lecture.
It says we measure from a point that is 280 feet from one end of the bridge, and 160 feet from the other.0817
I drew that point and I filled in the 160 and the 280.0825
Then it gave me the angle between those two lines, so I filled that in.0831
All of a sudden, I've got a standard triangle problem, and moreover, I've got a triangle problem where I know two sides and the angle between them, and what I want to find is the third side of the triangle.0835
Then, it's just a matter of simplifying down the numbers until you get an answer and figuring out that the units have to be square feet, because the original measurements in the problem were in terms of feet, and we're describing an area now, it must be square feet.1137