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 Preparation

Be prepared to display applets for all to see throughout the lesson.

Student Facing

• I can use trigonometry to solve problems.

Building Towards

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.

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