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# 13 4 tangent ratio lesson

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### 13 4 tangent ratio lesson

1. 1. Sec. 8 – 3Sec. 8 – 3 The Tangent RatioThe Tangent Ratio Objective:Objective: 1) To use tangent ratios to1) To use tangent ratios to determine side lengths indetermine side lengths in ΔΔ..
2. 2. This only for rightThis only for right ΔΔs!!s!!  TrigonometryTrigonometry  Greek WordGreek Word  Trigon → TriangleTrigon → Triangle  Metron → MeasureMetron → Measure  Trigonometry RatioTrigonometry Ratio – Ratio of the lengths of– Ratio of the lengths of sides of a rightsides of a right ΔΔ..
3. 3.  The tangent is just a button on your calculator!The tangent is just a button on your calculator! TanTan ** Make sure you calculator is in Degrees!!
4. 4. Tangent RatioTangent Ratio  Tangent RatioTangent Ratio – Ratio of the length of the– Ratio of the length of the opposite leg from anopposite leg from an ∠∠ to the length of the legto the length of the leg adjacent to the sameadjacent to the same ∠∠.. A C B b a c * Can’t use the right ∠, ∠C Tangent ∠A = Length of leg Opposite of ∠A Length of leg Adjacent of ∠A Tangent ∠A = a b
5. 5. Writing tangent ratiosWriting tangent ratios  Write the tangent ratio ofWrite the tangent ratio of ∠∠T andT and ∠∠U.U. T U S 6 8 10 Tangent ∠θ = Opposite Adjacent Tangent ∠T = 8 6 TS US = Tangent ∠U =TS US 6 8= ** Tangent ratio for ∠T & ∠U are reciprocals
6. 6. You can use the tangent ratio to findYou can use the tangent ratio to find the measure of a distance that isthe measure of a distance that is difficult to measure directly.difficult to measure directly.  Example 1: Find w.Example 1: Find w. 10 w 54 Step 1: Set up the Tangent Ratio Tan 54 = opp adj Tan 54 = w 10 1.376 = w 10 13.76 = w
7. 7. Ex. 2: Solve for the variable usingEx. 2: Solve for the variable using the tangent ratio.the tangent ratio. 70° 8cm x Step 1: Set up the tangent ratio. Tan 70 = opp adj Tan 70 = 8 x 2.747 = 8 x Multiply both sides by the denominator, x 2.747x = 8 x = 2.9
8. 8. The Tangent Inverse: TanThe Tangent Inverse: Tan-1-1  Just another button on your Calculator!Just another button on your Calculator!  Use it when you have the two sides of aUse it when you have the two sides of a ΔΔ andand are trying to find a missingare trying to find a missing ∠∠.. TanTan Tan-1Use the SHIFT (2nd ) Key to get to it. Once you press it, it should look like this: Tan-1 (
9. 9. Ex.3: Using the TanEx.3: Using the Tan-1-1  Use the TanUse the Tan-1-1 to solve for the missingto solve for the missing ∠∠.. 12mm 5mm y° Step 1: Set up the Tan Ratio Tan y = opp adj Tan y = 5 12 Tan y = .4167 At this point you will use the Tan-1 : 1) Hit shift Tan to get to Tan-1 ( 2) Type in the decimal and hit enter Tan-1 (.4167) = 22.6°
10. 10. Ex.4: Solve for mEx.4: Solve for m∠∠ZZ 8miles8miles 6miles6miles x Y Z Tan Z = opp adj Tan Z = 8 6 Tan Z = 1.333 Tan-1 (1.333) = m∠Z m∠Z = 53.1°
11. 11. What have I learned???What have I learned???  TanTan θθ ==  Use TanUse Tan-1-1 when looking for anwhen looking for an ∠∠ measure.measure. Opposite Side Adjacent Side