Lesson 10
Solving Problems with Trigonometry
Lesson Narrative
In this lesson students apply the concepts of trigonometry to two different situations. In the first, students need to interpret a diagram with limited information to find a way to calculate the dimensions of a polygon. In the second, students are given information about a plane’s flight path, but they need to draw their own diagram as well as grapple with converting units. In each of these situations, students are making sense of problems (MP1) before they are able to use trigonometry to solve the problem.
Learning Goals
Teacher Facing
 Use trigonometry to solve problems (using words and other representations).
Student Facing
 Let’s solve problems about right triangles.
Required Materials
Required Preparation
Be prepared to display applets for all to see throughout the lesson.
Learning Targets
Student Facing
 I can use trigonometry to solve problems.
CCSS Standards
Glossary Entries

arccosine
The arccosine of a number between 0 and 1 is the acute angle whose cosine is that number.

arcsine
The arcsine of a number between 0 and 1 is the acute angle whose sine is that number.

arctangent
The arctangent of a positive number is the acute angle whose tangent is that number.

cosine
The cosine of an acute angle in a right triangle is the ratio (quotient) of the length of the adjacent leg to the length of the hypotenuse. In the diagram, \(\cos(x)=\frac{b}{c}\).

sine
The sine of an acute angle in a right triangle is the ratio (quotient) of the length of the opposite leg to the length of the hypotenuse. In the diagram, \(\sin(x) = \frac{a}{c}.\)

tangent
The tangent of an acute angle in a right triangle is the ratio (quotient) of the length of the opposite leg to the length of the adjacent leg. In the diagram, \(\tan(x) = \frac{a}{b}.\)

trigonometric ratio
Sine, cosine, and tangent are called trigonometric ratios.