1. Sec. 8 – 3 The Tangent Ratio

2. Objectives/DFA/HW
Objective: SWBAT use the tangent ratios to determine side lengths in triangles.
DFA: p.434 #6bjecti
HW: pp (2-28 even, even)s pp (2-28 even, even)

3. This only for right Δs!! Trigonometry
Greek Word
Trigon → Triangle
Metron → Measure
Trigonometry Ratio – Ratio of the lengths of sides of a right Δ.

4. Tan ** Make sure you calculator is in Degrees!!
The tangent is just a button on your calculator!
Tan
** Make sure you calculator is in Degrees!!

5. Tangent Ratio * Can’t use the right , C c b a A B C
Tangent Ratio – Ratio of the length of the opposite leg from an  to the length of the leg adjacent to the same . A
* Can’t use the right , C
Length of leg Opposite of A
Tangent A = c
Length of leg Adjacent of A b a
Tangent A = b B C a

6. Writing tangent ratios
Write the tangent ratio of T and U. U
Opposite 10
Tangent  = 6
Adjacent T S 8 TS 8 US 6
Tangent U = =
Tangent T = = 6 US TS 8
** Tangent ratio for T & U are reciprocals

7. You can use the tangent ratio to find the measure of a distance that is difficult to measure directly.
Example 1: Find w.
Step 1: Set up the Tangent Ratio
opp 10
Tan 54 =
adj 54 w
Tan 54 = 10 w w
1.376 = 10
13.76 = w

8. Ex. 2: Solve for the variable using the tangent ratio.
Step 1: Set up the tangent ratio.
opp
Tan 70 =
adj
8cm 8
Tan 70 = x
70° 8 x
2.747 = x
Multiply both sides by the denominator, x
2.747x = 8
x = 2.9

9. The Tangent Inverse: Tan-1
Just another button on your Calculator!
Use it when you have the two sides of a Δ and are trying to find a missing .
Tan-1
Use the SHIFT (2nd) Key to get to it.
Tan
Once you press it, it should look like this:
Tan-1 (

10. Ex.3: Using the Tan-1 12mm y° 5mm
Use the Tan-1 to solve for the missing .
12mm y°
5mm
Step 1: Set up the Tan Ratio
At this point you will use the Tan-1:
Hit shift Tan to get to
Tan-1(
2) Type in the decimal and hit enter
opp
Tan y =
adj 5
Tan y = 12
Tan y = .4167
Tan-1 (.4167) =
22.6°

11. Ex.4: Solve for mZ opp Tan Z = adj 8 Tan Z = 6 6 miles Tan Z = 1.333
Tan-1 (1.333) = mZ
mZ = 53.1° x Y
8miles

12. What have I learned??? Opposite Side Adjacent Side Tan  =
Use Tan-1 when looking for an  measure.
Opposite Side
Adjacent Side