1. Using Tangent, Sine and Cosine to find Sides of RIGHT TRIANGLES
MODULE B- LESSON 5

2. 1) Highlight sides of Right Triangle
Hypotenuse, color right angle, highlight side across from right angle
Adjacent, color given angle, highlight side touching it
Opposite, highlight side opposite given angle
38o

3. 2) Pick which tool to use x 15o 10 5 x 12o 20 17o x
Reminder θ is a variable we use to represent the given angle!
Tangent (TOA)
Tanθ= Opposite
1 Adjacent
Sine (SOH)
Sinθ= Opposite
Hypotenuse
Cosine (CAH)
Cosθ= Adjacent
15o x 10
12o 5 x
17o 20 x

4. 3) Solve for Missing Side
How?
Cross multiply and divide!!
Round answers to the nearest tenth

5. Tangent- Example 1 (x on top)
Q1 on your handout
Tanθ= Opposite
Adjacent
Tan(18º)= x
Cross multiply
12(Tan18) = x
x = 3.9
18o x 12

6. Tangent- Example 2 (x on bottom)
Not on your handout
Tanθ= Opposite
1 Adjacent
Tan(8º)= 14 x
Cross multiply
x(Tan8) = 14
divide both sides by (Tan38) to get x alone
x = 14
(Tan8)
x = 99.6 8o 14 x

7. Sine- Example 1 (x on top)
Q1 on your handout
Sinθ= Opposite
1 Hypotenuse
Sin(12º)= x
Cross multiply
5(Sin12) = x
x = 1.0 5 x
12o

8. Sine- Example 2 (x on bottom)
Not on your handout
Sinθ= Opposite
1 Hypotenuse
Sin(38º)= 18 x
Cross multiply
x(Sin38) = 18
divide both sides by (Sin38) to get x alone
x = 18
(Sin38)
x = 29.2 18 x
38o

9. Cosine- Example 1 (x on top)
Q1 on your handout
Cosθ= Adjacent
Hypotenuse
Cos(17º)= x
Cross multiply
20(Cos17) = x
x = 19.1 20
17o x

10. Cosine- Example 2 (x on bottom)
Q7 on your handout
Cosθ= Adjacent
Hypotenuse
Cos(16º)= 23 x
Cross multiply
X(Cos16) = 23
divide both sides by (Cos16) to get x alone
X = 23
(Cos16)
X = 23.9 x
16o 23

11. Review: All Right Triangle Tools
Pythagorean Theorem
(a2 + b2 = c2)
c must be the hypotenuse
Need: 2 sides
Finds: 3rd side
SOHCAHTOA
(sine, cosine, tangent ratios)
Need: 1 side, 1 angle
Finds: 1 additional side