Geometry – Chapter 13 Lesson Plans
Section 13.4 – Tangent Ratio
Enduring Understandings: The student shall be able to:
- Use the tangent ratio to solve problems.
Standards:
28. Right Triangles
Identifies and evaluates tangent, sine, and cosine ratios for an acute angle of a right triangle; uses a table, calculator, or computer to find the ratio for a given angle or find the angle for a given ratio.
29. Right Triangles
Uses the tangent, sine, and cosine ratios for right triangles to solve application problems such as indirect-measurement problems
Essential Questions: What is the “tangent” ratio, and how do we use it to find unknown distances?
Warm up/Opener:
Start with two similar triangles with sides 3, 4, and 5, and sides 4.5, 6, and 7.5. Let ÐA and ÐB be the vertex of the short leg and the hypotenuse of the respective triangles. Find the ratio of the opposite leg divided by the adjacent leg. They should be the same number.
Activities:
We are starting to use trigonometry.
A Trigonometric ratio is a ratio of the measures of two sides of a right triangle.
Definition of Tangent: If A is an acute angle of a right triangle, then
tan A = measure of leg opposite of ÐA
measure of the leg adjacent to ÐA
Make sure your calculator mode is in degrees.
If you know the angle A and one leg you can calculate the other leg:
Tan 40 = measure of the opposite leg/23
Therefore, the measure of the opposite leg = 23 * tan 40 = 19.3
You can also find the measure of the degree of the angle by using the inverse tan key:
Tan A = 4/5
A = Tan-1 4/5 = 38.7 degrees
Tan A = 1/Ö3 Þ A = Tan-1 1/Ö3 = 30
Tan B = Ö3/1 Þ B = Tan-1 Ö3/1 = 60
Angle of elevation is the angle made by the line of sight to a higher elevation and horizontal.
Angle of depression is the angle made by the line of sight to a lower elevation and horizontal.
Assessments:
Do the “Check for Understanding”
CW WS 13.4
HW pg 568 – 569, # 9 – 23 all (15)