1. 9.2 Trigonometry: Tangent Ratio Day 1
Geometry
9.2 Trigonometry: Tangent Ratio
Day 1

2. SOH-CAH-TOA
In a right triangle, there are three sides, two acute angles, and a right angle
From either acute angle, there is an opposite leg, an adjacent leg and the hypotenuse
A leg of a right triangle is a side that forms the right angle
The hypotenuse is always opposite the right angle

3. SOH-CAH-TOA A
Hypotenuse
Opposite Leg C
Adjacent Leg B

4. SOH-CAH-TOA A
Hypotenuse
Adjacent Leg C
Opposite Leg B

5. 9.2 Tangent Ratio Tangent Ratio, Cotangent Ratio and Inverse Tangent
Objectives
Use the tangent ratio in a right triangle to solve for unknown sides lengths.
Use the cotangent ratio in a right triangle to solve for unknown sides lengths.
Relate the tangent ratio to the cotangent ratio.
Use the inverse tangent in a right triangle to solve for unknown angle measures.
SOH – CAH – TOA

7. 9.2 Problem 2 Slope and Right Triangles
Pg. 672 Collaborate 1-6 (8 Minutes)
The TANGENT (TAN) of an acute angle in a right triangle is the ratio of the length of the side that is opposite the reference angle to the length of the side that is adjacent to the reference angle.
Collaborate 7-10 (6 Minutes)
Collaborate (5 Minutes)

8. 9.2 Problem 2 Slope and Right Triangles
12.

9. 9.2 Problem 2 Slope and Right Triangles
13.
Together #14

10. 9.2 Problem 4 Cotangent Ratio
The cotangent of an angle is the reciprocal of the tangent of an angle.
The COTANGENT (COT) of an acute angle in a right triangle is the ratio of the length of the adjacent leg to the length of the opposite leg in relation to the angle used.
We can always use the tangent function.

11. 9.2 Problem 4 Cotangent Ratio
On the calculator
There is no cotangent button
COT is the reciprocal of TAN
cot 𝜃 = 1 tan 𝜃
Example
𝐹𝑖𝑛𝑑 cot 35 𝑜
= 1 tan 35 𝑜 ≈1.43

12. Review Tangent Day 1
What is the ratio of sides in a right triangle for the tangent function?
Opposite over Adjacent
What is the ratio of sides in a right triangle for the cotangent function?
Adjacent over Opposite

13. 9.2 Trigonometry: Tangent Ratio Day 2
Geometry
9.2 Trigonometry: Tangent Ratio
Day 2

14. Review Tangent Day 1
What is the ratio of sides in a right triangle for the tangent function?
Opposite over Adjacent
What is the ratio of sides in a right triangle for the cotangent function?
Adjacent over Opposite

15. 9.2 Tangent Ratio Tangent Ratio, Cotangent Ratio and Inverse Tangent
Objectives
Use the tangent ratio in a right triangle to solve for unknown sides lengths.
Use the cotangent ratio in a right triangle to solve for unknown sides lengths.
Relate the tangent ratio to the cotangent ratio.
Use the inverse tangent in a right triangle to solve for unknown angle measures.
SOH – CAH – TOA

16. 9.2 Problem 5 Inverse Tangent
The inverse tangent (arc tangent or 𝑡𝑎𝑛 −1 ) is the measure of an acute angle whose tangent is x.
The relationship of sides used is opposite to adjacent.
The calculator has an inverse tangent function.
Only used to find the missing angle.

17. 9.2 Problem 5 Inverse Tangent
Collaborate 1-3 (5 Minutes)

18. 9.2 Problem 5 Inverse Tangent

19. 9.2 Problem 5 Inverse Tangent3.

20. Problem 6: Road Grades How can we write 8% a different way? 0.08 8 100
Collaborate 1-5 (5 Minutes)

21. The diagram is not “proportional” to 8%
Problem 6: Road Grades 3.
𝑡𝑎𝑛 − = 𝑡𝑎𝑛 − ≈ 3.43 𝑜 4.
tan 10 ≈0.176≈17.6%
Should read 18% 5. No
The diagram is not “proportional” to 8%

22. tan 𝜃 = 𝑂𝑝𝑝𝑜𝑠𝑖𝑡𝑒 𝐴𝑑𝑗𝑎𝑐𝑒𝑛𝑡
𝑥=2200 𝑓𝑡
Does it make sense that the
two sides of the triangle are equal?
Yes: Isosceles, Right Triangle
45 𝑜
Adjacent X
Opposite

23. Use the given diagram to find the missing side
100 ft
28 𝑜 X
tan 28 = 100 𝑥
𝑥 tan 28 =100
𝑥= 100 tan 28 ≈ 𝑓𝑒𝑒𝑡
Shortcut
tan 28 = 100 𝑥
𝑆𝑤𝑖𝑡𝑐ℎ
𝑥= 100 tan 28 ≈ 𝑓𝑒𝑒𝑡

24. Formative Assessment SOH-CAH-TOA
Skills Practice 9.2: The Tangent Ratio
Vocabulary
Pg. 677 (1-3)
Problem Set
Pg (1-43) odd
tan 𝜃 = 𝑂𝑝𝑝𝑜𝑠𝑖𝑡𝑒 𝐿𝑒𝑔 𝐴𝑑𝑗𝑎𝑐𝑒𝑛𝑡 𝐿𝑒𝑔
SOH-CAH-TOA
Check the MODE on the calculators
The MODE must be in DEGREES