Sec. 8 – 3 The Tangent Ratio

Objectives/DFA/HW Objective: SWBAT use the tangent ratios to determine side lengths in triangles. DFA: p.434 #6bjecti HW: pp.434-437 (2-28 even, 48-64 even)s pp.434-436 (2-28 even, 48-58 even)

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

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!!

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

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

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

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

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 (

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°

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

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