Download 13.5 Sine and Cosine Ratios

Geometry – Chapter 13 Lesson Plans
Section 13.5 – Sine and Cosine Ratios
Enduring Understandings: The student shall be able to:
1. Use the sine and cosine ratios 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 are the “sine” and “cosine” ratios, and how do we use them to
find unknown distances?
Warm up/Opener:
Activities:
We discussed tangent ratio in Section 13-4 as being the ratio of the length of the opposite
side divided by the length of the adjacent side. The ratios of the other sides also have
names, specifically:
Sine = length of opposite side/length of hypotenuse
Cosine = length of adjacent side/length of hypotenuse.
Do some examples of finding sine and cosine. Specifically, fine sine of A and cosine of
B:
B
A
We can also find the measure of the angles by taking inverse sine or inverse cosine.
What is sine/cosine? (answer – tangent)
If we know the triangle is a right triangle, we can now use the trigonometric functions of
sine, cosine and tangent and what we already know about the sum of the internal angles
of a triangle equal 180, to calculate the unknown angle and lengths of sides if we only
know the measure of one other angle and the measure of one side. This is pretty
powerful stuff and has many uses in life. It is usually much easier to measure one angle
and one length and calculate the others than it is to measure them all.
Assessments:
Do the “Check for Understanding”
CW WS 13.5
HW pg 576 # 13 – 41 odd (15)