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Lesson 9.1 Use Trigonometry with Right Triangles. Standard Accessed: Students will prove, apply, and model trigonometric functions and ratios. Warm-Up. Lesson Presentation. Lesson Quiz. Warm-Up.

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Lesson 9.1Use Trigonometry with Right TrianglesStandard Accessed: Students will prove, apply, and model trigonometric functions and ratios.Warm-UpLesson PresentationLesson QuizWarm-UpIn right triangle ABC, a and b are the lengths of the legs and c is the length of the hypotenuse. Find the missing length. Give exact values.1. 2.3.If you walk 2.0 kilometers due east and then 1.5 kilometers due north, how far will you be from your starting point. 1. distance formulaVocabularyEssential UnderstandingsHow are trigonometric functions used in right triangles?The six trigonometric ratios: sine, cosine, tangent, cosecant, secant, and cotangent, are the six possible ratios of pairs of sides of a right triangle. If you know the length of any side and the measure of either of the acute angles, you can find all the remaining parts of a right triangle. 1EXAMPLEEvaluate trigonometric functionsEvaluate the six trigonometric functions of the angle .25SOLUTION3. 1. 2. 6. 4. 5. 2EXAMPLEEvaluate trigonometric functionsIf is an acute angle of a right triangle and , what is the value of ?SOLUTIONa. b. c. d. Geometry ConjecturesIsosceles Right Triangle:In an isosceles right triangle, if the legs have length , then the hypotenuse has length .:In a triangle, if the shorter leg has length , then the longer leg has length and the hypotenuse has length .Vocabulary3EXAMPLEFind an unknown side length of a right triangleFind the value for in the right triangle shown.SOLUTIONGeometry Isosceles Conj.4EXAMPLEUse a calculator to solve a right triangleSolve .=20SOLUTION4EXAMPLEUsing indirect MeasurementHiking in Nepal You are hiking toward Machapuchare “Fish Tail” in the Annapurna range, but you reach a point where an avalanche has destroyed the trail (1). To avoid the avalanche, you take an alternative trail route. You turn onto a diagonal trail (2) that meets your original trail at a 48° angle and follow that trail for 3.6 miles until you hit another trail (3) that intersects back with your original trail at a 90° angle. How far were you from the intersection of your trail (1) and trail (3) when you turned onto the diagonal trail (2)? How far will you travel taking the alternative trail route around the avalanche?≈ 2.4 miYou will travel ≈ 6.3 mi around the avalanche.5EXAMPLEUsing Angle of ElevationKIS Flagpole You measure from a point on the ground 28 feet from the base of the KIS flagpole, the angle of elevation to the top of the flagpole is 63°. Estimate the height of the flagpole.SOLUTIONThe approximate height of the KIS flagpole is 55 feet.Lesson 9.1 Homework:Practice B Practice C “Honors”

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