Download Geometry Fall 2011 Lesson 17 (S.A.S. Postulate)

1
Lesson Plan #75
Date: Thursday March 19th, 2015
Class: Geometry
Topic: Sine, cosine and tangent ratios.
Aim: How can we find sine, cosine and tangent ratios?
Objectives:
1) Students will be able to find sine, cosine and tangent ratios.
HW # 75:
Page 308 #’s 1, 4, 7, 10, 13
Page 314 #’s 1, 4, 7, 10, 13
Do Now:
1)
PROCEDURE:
Write the Aim and Do Now
Get students working!
Take attendance
Give Back HW
Collect HW
Go over the Do Now
4
2√3
Assignment #1:
What relationship exists between the two right triangles at right?
2
Let’s focus on the 60o angle of the smaller right triangle. What is the length of the side opposite the 60o angle?
What is the length of the side adjacent to the 60o angle?
What is the ratio of the length of the side opposite the 60 o angle to the side adjacent to the 60o angle?
Looking at the bigger right triangle, what is the ratio of the length of the side opposite the 60 o angle to the side adjacent to the 60o
angle?
This ratio will be constant for a 60o angle in any right triangle, no matter how large or how small the sides of the triangle are.
The ratio of the side opposite an acute angle to the side adjacent to the same acute angle in a right triangle is called a tangent ratio.
In the diagram above, find the tangent of 30 o (tan 30o) .
𝑡𝑎𝑛𝐴 =
𝑜𝑝𝑝𝑜𝑠𝑖𝑡𝑒
𝑎𝑑𝑗𝑎𝑐𝑒𝑛𝑡
Other Ratios:
Aside from the tangent ratio, there are other ratios we can form in the right triangle. For example we could form the ratio of the
side opposite an acute angle to the hypotenuse of the right triangle. This ratio is called the sine ratio.
In the above triangles, find sin 30o.
Find sin 60o.
𝑠𝑖𝑛𝐴 =
𝑜𝑝𝑝𝑜𝑠𝑖𝑡𝑒
ℎ𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒
𝑐𝑜𝑠𝐴 =
𝑎𝑑𝑗𝑎𝑛𝑐𝑒𝑛𝑡
ℎ𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒
In a right triangle, the ratio of the length of the side adjacent to the an acute angle to the length of
the hypotenuse is called the cosine of that acute angle.
In the above triangles, find cos 30o.
Find cos 60o.
To help remember these ratios, use the mnemonic SOH CAH TOA
2
In the triangle at right find
A) sin 45o
B) cos 45o
C) tan 45o
The 30o, 60o, 45o angles are called special angles. To find the trig ratios of angles other than the
special angles, we can use a table of trig values or we can use our calculator.
3
4
Sample Test Questions:
1)
2)
3)
4)
5)
6)