THE Tangent Ratio Unit 10: Section 8.5 Objective: To Define the tangent ratio for an acute Triangle. To Solve Right Triangle problems using the tangent ratio.

Find the tangent, sine, and cosine keys on the calculator. Trigonometry Trignometry – comes from the Greek words that mean “triangle measurement. Our Study will be limited to the trigonometry of Right Triangle. Purpose (video link) : Introduce the very important ratio, called the tangent ratio, that is formed by using the lengths of the legs of a right triangle. BUT FIRST – EVERYONE NEEDS A CALCULATOR Find the tangent, sine, and cosine keys on the calculator.

Find the inverse tangent, sine, and cosine keys on the calculator. Example 1: Use a calculator to find the value of each to the nearest ten-thousandth. 1) sin 21° 2) tan 22° Practice 1: Use a calculator to find the value of each to the nearest ten-thousandth. cos 20° 2) sin 77° 3) tan 17° 4) cos 87° Find the inverse tangent, sine, and cosine keys on the calculator.

Example 2: Find each angle measure to the nearest degree. 1) sin B = 0.4848 2) cos W = 0.6157 3) tan W = 19.0811 Practice 2: Find each angle measure to the nearest degree. sin A = 0.5150 2) cos A = 0.7431 3) cos A = 0.5878 4) cos A = 0.4226 5) tan W = 0.5317 6) sin A = 0.7431 Extra Practice: tan 24° = _________ 2) tan 41° = _________ 3) tan 88° = _________ 4) tan ______ = 2.4751 5) tan ______ = 0.3057 6) tan ______ = 0.8098

THE TANGENT RATIO NOW INTRODUCING Side Adjacent ∠x Tangent ∠x = Side Opposite ∠x Side Adjacent ∠x

Side Adjacent ∠x Tangent ∠x = Side Opposite ∠x Side Adjacent ∠x x

Practice 70° 29.24 10 90° 20° 27.47 Using the given triangle, find the following measures to the nearest hundredth.   leg opposite 20° 2) tangent 20° leg adjacent 20° 3) leg opposite 70° 4) tangent 70° leg adjacent 70°

USING THE TANGENT RATIO Use the tan proportion to solve the following. Example 3 x 37° 12 13.5 80° x

Guided Practice: Find tan A, tan B, m∠A, and m∠B 1. 2. Find the value of x to the nearest tenth. 7 C A 2 A B 17 15 B C 8 20 24° x

Guided Practice: Find the value of x to the nearest tenth 4. Find y° correct to the nearest degree. 5. 6. 10 35° x 8 5 y° 8 6 y° 10

Closure: What the name of the branch of mathematics that uses tangents, cosines, and sines? State the tangent ratio. Homework: P308 Written Exercises: #1-18a